R/ecdftoj.R
In tkhdyanagi/panelhetero: Panel Data Analysis with Heterogeneous Dynamics
Defines functions
toj5_boot
toj4_boot
toj3_boot
toj2_boot
toj1_boot
toj0_boot
tojecdf
Documented in
tojecdf
#' The TOJ bias-corrected empirical CDF estimation
#'
#' The `tojecdf()` function enables to implement the TOJ bias-corrected
#' estimation of the cumulative distribution function (CDF) of
#' the heterogeneous mean, the heterogeneous autocovariance, and
#' the heterogeneous autocorrelation.
#' The method is developed by Okui and Yanagi (2019).
#' For more details, see the package vignette with `vignette("panelhetero")`.
#'
#' @param data A matrix of panel data.
#' Each row corresponds to individual time series.
#' @param acov_order A non-negative integer of the order of autocovariance.
#' Default is 0.
#' @param acor_order A positive integer of the order of autocorrelation.
#' Default is 1.
#' @param ci A logical whether to estimate the confidence interval.
#' Default is TRUE.
#' @param R A positive integer of the number of bootstrap repetitions.
#' Default is 1000.
#'
#' @returns A list that contains the following elements.
#' \item{mean}{A plot of the corresponding CDF}
#' \item{acov}{A plot of the corresponding CDF}
#' \item{acor}{A plot of the corresponding CDF}
#' \item{mean_func}{A function that returns the corresponding CDF}
#' \item{acov_func}{A function that returns the corresponding CDF}
#' \item{acor_func}{A function that returns the corresponding CDF}
#' \item{mean_ci_func}{A function that returns the 95 percent confidence
#' interval for the corresponding CDF}
#' \item{acov_ci_func}{A function that returns the 95 percent confidence
#' interval for the corresponding CDF}
#' \item{acor_ci_func}{A function that returns the 95 percent confidence
#' interval for the corresponding CDF}
#' \item{quantity}{A matrix of the estimated heterogeneous quantities}
#' \item{acov_order}{The order of autocovariance}
#' \item{acor_order}{The order of autocorrelation}
#' \item{N}{The number of cross-sectional units}
#' \item{S}{The length of time series}
#' \item{R}{The number of bootstrap repetitions}
#'
#' @examples
#' data <- panelhetero::simulation(N = 300, S = 50)
#' panelhetero::tojecdf(data = data, R = 50)
#'
#' @references Okui, R. and Yanagi, T., 2019.
#' Panel data analysis with heterogeneous dynamics.
#' Journal of Econometrics, 212(2), pp.451-475.
#'
#' @export
#'
tojecdf <- function(data,
acov_order = 0,
acor_order = 1,
R = 1000,
ci = TRUE) {
# Error handling -------------------------------------------------------------
error1(data = data,
acov_order = acov_order,
acor_order = acor_order,
R = R)
# Variable definitions -------------------------------------------------------
x <- y <- NULL
# Omit NA
data <- stats::na.omit(data)
# Sample size
N <- nrow(data)
S <- ncol(data)
# Estimated means, autocovariances, autocorrelations
mean_est <- rowMeans(data)
acov_est <- apply(data, MARGIN = 1, acov, acov_order = acov_order)
acor_est <- apply(data, MARGIN = 1, acor, acor_order = acor_order)
# TOJ bias-corrected estimation ----------------------------------------------
if (S %% 6 == 0) {
# Split panel data for T equivalent to 0 modulo 6
data21 <- data[, 1:(S / 2)]
data22 <- data[, (S / 2 + 1):S]
data31 <- data[, 1:(S / 3)]
data32 <- data[, (S / 3 + 1):(2*S / 3)]
data33 <- data[, (2 * S / 3 + 1):S]
# Estimated quantities for split panel data
mean_est21 <- rowMeans(data21)
mean_est22 <- rowMeans(data22)
mean_est31 <- rowMeans(data31)
mean_est32 <- rowMeans(data32)
mean_est33 <- rowMeans(data33)
acov_est21 <- apply(data21, MARGIN = 1, acov, acov_order = acov_order)
acov_est22 <- apply(data22, MARGIN = 1, acov, acov_order = acov_order)
acov_est31 <- apply(data31, MARGIN = 1, acov, acov_order = acov_order)
acov_est32 <- apply(data32, MARGIN = 1, acov, acov_order = acov_order)
acov_est33 <- apply(data33, MARGIN = 1, acov, acov_order = acov_order)
acor_est21 <- apply(data21, MARGIN = 1, acor, acor_order = acor_order)
acor_est22 <- apply(data22, MARGIN = 1, acor, acor_order = acor_order)
acor_est31 <- apply(data31, MARGIN = 1, acor, acor_order = acor_order)
acor_est32 <- apply(data32, MARGIN = 1, acor, acor_order = acor_order)
acor_est33 <- apply(data33, MARGIN = 1, acor, acor_order = acor_order)
# Function for bootstrap confidence interval
mean_ci_func <- Vectorize(FUN = function(x) {
# TOJ bias-corrected estimation with bootstrap
bootstrap <- boot::boot(data = cbind(mean_est,
mean_est21,
mean_est22,
mean_est31,
mean_est32,
mean_est33) - x,
statistic = toj0_boot,
R = R)
estimate <- bootstrap$t0
temp <- bootstrap$t- bootstrap$t0
# Confidence interval
quantile <- apply(temp,
MARGIN = 2,
stats::quantile,
probs = c(0.025, 0.975))
l_ci <- max(0, estimate + quantile[1])
u_ci <- min(1, estimate + quantile[2])
ci <- cbind(l_ci, u_ci)
colnames(ci) <- c("95% CI lower", "95% CI upper")
return(ci)
}, vectorize.args = "x")
acov_ci_func <- Vectorize(FUN = function(x) {
# TOJ bias-corrected estimation with bootstrap
bootstrap <- boot::boot(data = cbind(acov_est,
acov_est21,
acov_est22,
acov_est31,
acov_est32,
acov_est33) - x,
statistic = toj0_boot,
R = R)
estimate <- bootstrap$t0
temp <- bootstrap$t- bootstrap$t0
# Confidence interval
quantile <- apply(temp,
MARGIN = 2,
stats::quantile,
probs = c(0.025, 0.975))
l_ci <- max(0, estimate + quantile[1])
u_ci <- min(1, estimate + quantile[2])
ci <- cbind(l_ci, u_ci)
colnames(ci) <- c("95% CI lower", "95% CI upper")
return(ci)
}, vectorize.args = "x")
acor_ci_func <- Vectorize(FUN = function(x) {
# TOJ bias-corrected estimation with bootstrap
bootstrap <- boot::boot(data = cbind(acor_est,
acor_est21,
acor_est22,
acor_est31,
acor_est32,
acor_est33) - x,
statistic = toj0_boot,
R = R)
estimate <- bootstrap$t0
temp <- bootstrap$t- bootstrap$t0
# Confidence interval
quantile <- apply(temp,
MARGIN = 2,
stats::quantile,
probs = c(0.025, 0.975))
l_ci <- max(0, estimate + quantile[1])
u_ci <- min(1, estimate + quantile[2])
ci <- cbind(l_ci, u_ci)
colnames(ci) <- c("95% CI lower", "95% CI upper")
return(ci)
}, vectorize.args = "x")
# Limits used for ggplot2
mean_lim <- c(min(mean_est),
max(mean_est))
acov_lim <- c(min(acov_est),
max(acov_est))
acor_lim <- c(min(acor_est),
max(acor_est))
# Compute confidence intervals
if (ci) {
mean_grid <- seq(mean_lim[1], mean_lim[2], length.out = 101)
acov_grid <- seq(acov_lim[1], acov_lim[2], length.out = 101)
acor_grid <- seq(acor_lim[1], acor_lim[2], length.out = 101)
mean_ci <- mean_ci_func(mean_grid)
acov_ci <- acov_ci_func(acov_grid)
acor_ci <- acor_ci_func(acor_grid)
}
# Make figures using ggplot2
if (!ci) {
# Mean
mean_x <- seq(min(mean_est),
max(mean_est),
length = 101)
mean_y <- tojecdfest0(x = mean_x,
X = mean_est,
X21 = mean_est21,
X22 = mean_est22,
X31 = mean_est31,
X32 = mean_est32,
X33 = mean_est33)
mean_toj <- Rearrangement::rearrangement(x = data.frame(x = mean_x),
y = mean_y)
mean_plot <- ggplot2::ggplot(
data.frame(x = mean_x, y = mean_toj),
ggplot2::aes(x = x, y = y)
) +
ggplot2::geom_line() +
ggplot2::xlim(min(mean_est), max(mean_est)) +
ggplot2::ylim(0, 1) +
ggplot2::labs(x = "x", y = "") +
ggplot2::ggtitle("The heterogeneous mean") +
ggplot2::theme_bw()
# Autocovariance
acov_x <- seq(min(acov_est),
max(acov_est),
length = 101)
acov_y <- tojecdfest0(x = acov_x,
X = acov_est,
X21 = acov_est21,
X22 = acov_est22,
X31 = acov_est31,
X32 = acov_est32,
X33 = acov_est33)
acov_toj <- Rearrangement::rearrangement(x = data.frame(x = acov_x),
y = acov_y)
acov_plot <- ggplot2::ggplot(
data.frame(x = acov_x, y = acov_toj),
ggplot2::aes(x = x, y = y)
) +
ggplot2::geom_line() +
ggplot2::xlim(min(acov_est), max(acov_est)) +
ggplot2::ylim(0, 1) +
ggplot2::labs(x = "x", y = "") +
ggplot2::ggtitle("The heterogeneous autocovariance") +
ggplot2::theme_bw()
# Autocorrelation
acor_x <- seq(min(acor_est),
max(acor_est),
length = 101)
acor_y <- tojecdfest0(x = acor_x,
X = acor_est,
X21 = acor_est21,
X22 = acor_est22,
X31 = acor_est31,
X32 = acor_est32,
X33 = acor_est33)
acor_toj <- Rearrangement::rearrangement(x = data.frame(x = acor_x),
y = acor_y)
acor_plot <- ggplot2::ggplot(
data.frame(x = acor_x, y = acor_toj),
ggplot2::aes(x = x, y = y)
) +
ggplot2::geom_line() +
ggplot2::xlim(min(acor_est), max(acor_est)) +
ggplot2::ylim(0, 1) +
ggplot2::labs(x = "x", y = "") +
ggplot2::ggtitle("The heterogeneous autocorrelation") +
ggplot2::theme_bw()
}
if (ci) {
# Mean
mean_toj <- cbind(tojecdfest0(x = mean_grid,
X = mean_est,
X21 = mean_est21,
X22 = mean_est22,
X31 = mean_est31,
X32 = mean_est32,
X33 = mean_est33),
t(mean_ci))
mean_plot <- ggplot2::ggplot(
data = data.frame(x = mean_grid),
ggplot2::aes(x = mean_grid)
) +
ggplot2::geom_line(
ggplot2::aes(
x = mean_grid,
y = Rearrangement::rearrangement(
x = data.frame(x = mean_grid),
y = mean_toj[, 1]
)
)
) +
ggplot2::geom_ribbon(
ggplot2::aes(
x = mean_grid,
ymin = Rearrangement::rearrangement(
x = data.frame(x = mean_grid),
y = mean_toj[, 2]
),
ymax = Rearrangement::rearrangement(
x = data.frame(x = mean_grid),
y = mean_toj[, 3]
)
),
alpha = 0.1) +
ggplot2::labs(x = "x", y = "") +
ggplot2::ggtitle("The heterogeneous mean") +
ggplot2::ylim(0, 1) +
ggplot2::theme_bw()
# Autocovariance
acov_toj <- cbind(tojecdfest0(x = acov_grid,
X = acov_est,
X21 = acov_est21,
X22 = acov_est22,
X31 = acov_est31,
X32 = acov_est32,
X33 = acov_est33),
t(acov_ci))
acov_plot <- ggplot2::ggplot(
data = data.frame(x = acov_grid),
ggplot2::aes(x = acov_grid)
) +
ggplot2::geom_line(
ggplot2::aes(
x = acov_grid,
y = Rearrangement::rearrangement(
x = data.frame(x = acov_grid),
y = acov_toj[, 1]
)
)
) +
ggplot2::geom_ribbon(
ggplot2::aes(
x = acov_grid,
ymin = Rearrangement::rearrangement(
x = data.frame(x = acov_grid),
y = acov_toj[, 2]
),
ymax = Rearrangement::rearrangement(
x = data.frame(x = acov_grid),
y = acov_toj[, 3]
)
),
alpha = 0.1) +
ggplot2::labs(x = "x", y = "") +
ggplot2::ggtitle("The heterogeneous autocovariance") +
ggplot2::ylim(0, 1) +
ggplot2::theme_bw()
# Autocorrelation
acor_toj <- cbind(tojecdfest0(x = acor_grid,
X = acor_est,
X21 = acor_est21,
X22 = acor_est22,
X31 = acor_est31,
X32 = acor_est32,
X33 = acor_est33),
t(acor_ci))
acor_plot <- ggplot2::ggplot(
data = data.frame(x = acor_grid),
ggplot2::aes(x = acor_grid)
) +
ggplot2::geom_line(
ggplot2::aes(
x = acor_grid,
y = Rearrangement::rearrangement(
x = data.frame(x = acor_grid),
y = acor_toj[, 1]
)
)
) +
ggplot2::geom_ribbon(
ggplot2::aes(
x = acor_grid,
ymin = Rearrangement::rearrangement(
x = data.frame(x = acor_grid),
y = acor_toj[, 2]
),
ymax = Rearrangement::rearrangement(
x = data.frame(x = acor_grid),
y = acor_toj[, 3]
)
),
alpha = 0.1) +
ggplot2::labs(x = "x", y = "") +
ggplot2::ggtitle("The heterogeneous autocorrelation") +
ggplot2::ylim(0, 1) +
ggplot2::theme_bw()
}
# Functions without rearrangement
mean_func <- function(x) {
tojecdfest0(x = x,
X = mean_est,
X21 = mean_est21,
X22 = mean_est22,
X31 = mean_est31,
X32 = mean_est32,
X33 = mean_est33)
}
acov_func <- function(x) {
tojecdfest0(x = x,
X = acov_est,
X21 = acov_est21,
X22 = acov_est22,
X31 = acov_est31,
X32 = acov_est32,
X33 = acov_est33)
}
acor_func <- function(x) {
tojecdfest0(x = x,
X = acor_est,
X21 = acor_est21,
X22 = acor_est22,
X31 = acor_est31,
X32 = acor_est32,
X33 = acor_est33)
}
} else if (S %% 6 == 1) {
# Split panel data for T equivalent to 1 modulo 6
data21 <- data[, 1:floor(S / 2)]
data22 <- data[, (floor(S / 2) + 1):S]
data23 <- data[, 1:ceiling(S / 2)]
data24 <- data[, (ceiling(S / 2) + 1):S]
data31 <- data[, 1:floor(S / 3)]
data32 <- data[, (floor(S / 3) + 1):(2 * floor(S / 3))]
data33 <- data[, (2 * floor(S / 3) + 1):S]
data34 <- data[, 1:floor(S / 3)]
data35 <- data[, (floor(S / 3) + 1):(2 * floor(S / 3) + 1)]
data36 <- data[, (2 * floor(S / 3) + 2):S]
data37 <- data[, 1:ceiling(S / 3)]
data38 <- data[, (ceiling(S / 3) + 1):(2 * floor(S / 3) + 1)]
data39 <- data[, (2 * floor(S / 3) + 2):S]
# estimated quantities for split panel data
mean_est21 <- rowMeans(data21)
mean_est22 <- rowMeans(data22)
mean_est23 <- rowMeans(data23)
mean_est24 <- rowMeans(data24)
mean_est31 <- rowMeans(data31)
mean_est32 <- rowMeans(data32)
mean_est33 <- rowMeans(data33)
mean_est34 <- rowMeans(data34)
mean_est35 <- rowMeans(data35)
mean_est36 <- rowMeans(data36)
mean_est37 <- rowMeans(data37)
mean_est38 <- rowMeans(data38)
mean_est39 <- rowMeans(data39)
acov_est21 <- apply(data21, MARGIN = 1, acov, acov_order = acov_order)
acov_est22 <- apply(data22, MARGIN = 1, acov, acov_order = acov_order)
acov_est23 <- apply(data23, MARGIN = 1, acov, acov_order = acov_order)
acov_est24 <- apply(data24, MARGIN = 1, acov, acov_order = acov_order)
acov_est31 <- apply(data31, MARGIN = 1, acov, acov_order = acov_order)
acov_est32 <- apply(data32, MARGIN = 1, acov, acov_order = acov_order)
acov_est33 <- apply(data33, MARGIN = 1, acov, acov_order = acov_order)
acov_est34 <- apply(data34, MARGIN = 1, acov, acov_order = acov_order)
acov_est35 <- apply(data35, MARGIN = 1, acov, acov_order = acov_order)
acov_est36 <- apply(data36, MARGIN = 1, acov, acov_order = acov_order)
acov_est37 <- apply(data37, MARGIN = 1, acov, acov_order = acov_order)
acov_est38 <- apply(data38, MARGIN = 1, acov, acov_order = acov_order)
acov_est39 <- apply(data39, MARGIN = 1, acov, acov_order = acov_order)
acor_est21 <- apply(data21, MARGIN = 1, acor, acor_order = acor_order)
acor_est22 <- apply(data22, MARGIN = 1, acor, acor_order = acor_order)
acor_est23 <- apply(data23, MARGIN = 1, acor, acor_order = acor_order)
acor_est24 <- apply(data24, MARGIN = 1, acor, acor_order = acor_order)
acor_est31 <- apply(data31, MARGIN = 1, acor, acor_order = acor_order)
acor_est32 <- apply(data32, MARGIN = 1, acor, acor_order = acor_order)
acor_est33 <- apply(data33, MARGIN = 1, acor, acor_order = acor_order)
acor_est34 <- apply(data34, MARGIN = 1, acor, acor_order = acor_order)
acor_est35 <- apply(data35, MARGIN = 1, acor, acor_order = acor_order)
acor_est36 <- apply(data36, MARGIN = 1, acor, acor_order = acor_order)
acor_est37 <- apply(data37, MARGIN = 1, acor, acor_order = acor_order)
acor_est38 <- apply(data38, MARGIN = 1, acor, acor_order = acor_order)
acor_est39 <- apply(data39, MARGIN = 1, acor, acor_order = acor_order)
# Function for bootstrap confidence interval
mean_ci_func <- Vectorize(FUN = function(x) {
# TOJ bias-corrected estimation with bootstrap
bootstrap <- boot::boot(data = cbind(mean_est,
mean_est21,
mean_est22,
mean_est23,
mean_est24,
mean_est31,
mean_est32,
mean_est33,
mean_est34,
mean_est35,
mean_est36,
mean_est37,
mean_est38,
mean_est39) - x,
statistic = toj1_boot,
R = R)
estimate <- bootstrap$t0
temp <- bootstrap$t- bootstrap$t0
# Confidence interval
quantile <- apply(temp,
MARGIN = 2,
stats::quantile,
probs = c(0.025, 0.975))
l_ci <- max(0, estimate + quantile[1])
u_ci <- min(1, estimate + quantile[2])
ci <- cbind(l_ci, u_ci)
colnames(ci) <- c("95% CI lower", "95% CI upper")
return(ci)
}, vectorize.args = "x")
acov_ci_func <- Vectorize(FUN = function(x) {
# TOJ bias-corrected estimation with bootstrap
bootstrap <- boot::boot(data = cbind(acov_est,
acov_est21,
acov_est22,
acov_est23,
acov_est24,
acov_est31,
acov_est32,
acov_est33,
acov_est34,
acov_est35,
acov_est36,
acov_est37,
acov_est38,
acov_est39) - x,
statistic = toj1_boot,
R = R)
estimate <- bootstrap$t0
temp <- bootstrap$t- bootstrap$t0
# Confidence interval
quantile <- apply(temp,
MARGIN = 2,
stats::quantile,
probs = c(0.025, 0.975))
l_ci <- max(0, estimate + quantile[1])
u_ci <- min(1, estimate + quantile[2])
ci <- cbind(l_ci, u_ci)
colnames(ci) <- c("95% CI lower", "95% CI upper")
return(ci)
}, vectorize.args = "x")
acor_ci_func <- Vectorize(FUN = function(x) {
# TOJ bias-corrected estimation with bootstrap
bootstrap <- boot::boot(data = cbind(acor_est,
acor_est21,
acor_est22,
acor_est23,
acor_est24,
acor_est31,
acor_est32,
acor_est33,
acor_est34,
acor_est35,
acor_est36,
acor_est37,
acor_est38,
acor_est39) - x,
statistic = toj1_boot,
R = R)
estimate <- bootstrap$t0
temp <- bootstrap$t- bootstrap$t0
# Confidence interval
quantile <- apply(temp,
MARGIN = 2,
stats::quantile,
probs = c(0.025, 0.975))
l_ci <- max(0, estimate + quantile[1])
u_ci <- min(1, estimate + quantile[2])
ci <- cbind(l_ci, u_ci)
colnames(ci) <- c("95% CI lower", "95% CI upper")
return(ci)
}, vectorize.args = "x")
# Limits used for ggplot2
mean_lim <- c(min(mean_est),
max(mean_est))
acov_lim <- c(min(acov_est),
max(acov_est))
acor_lim <- c(min(acor_est),
max(acor_est))
# Compute confidence intervals
if (ci) {
mean_grid <- seq(mean_lim[1], mean_lim[2], length.out = 101)
acov_grid <- seq(acov_lim[1], acov_lim[2], length.out = 101)
acor_grid <- seq(acor_lim[1], acor_lim[2], length.out = 101)
mean_ci <- mean_ci_func(mean_grid)
acov_ci <- acov_ci_func(acov_grid)
acor_ci <- acor_ci_func(acor_grid)
}
# Make figures using ggplot2
if (!ci) {
# Mean
mean_x <- seq(min(mean_est),
max(mean_est),
length = 1000)
mean_y <- tojecdfest1(x = mean_x,
X = mean_est,
X21 = mean_est21,
X22 = mean_est22,
X23 = mean_est23,
X24 = mean_est24,
X31 = mean_est31,
X32 = mean_est32,
X33 = mean_est33,
X34 = mean_est34,
X35 = mean_est35,
X36 = mean_est36,
X37 = mean_est37,
X38 = mean_est38,
X39 = mean_est39)
mean_toj <- Rearrangement::rearrangement(x = data.frame(x = mean_x),
y = mean_y)
mean_plot <- ggplot2::ggplot(data.frame(x = mean_x, y = mean_toj),
ggplot2::aes(x = x, y = y)) +
ggplot2::geom_line() +
ggplot2::xlim(min(mean_est), max(mean_est)) +
ggplot2::ylim(0, 1) +
ggplot2::labs(x = "x", y = "") +
ggplot2::ggtitle("The heterogeneous mean") +
ggplot2::theme_bw()
# Autocovariance
acov_x <- seq(min(acov_est),
max(acov_est),
length = 1000)
acov_y <- tojecdfest1(x = acov_x,
X = acov_est,
X21 = acov_est21,
X22 = acov_est22,
X23 = acov_est23,
X24 = acov_est24,
X31 = acov_est31,
X32 = acov_est32,
X33 = acov_est33,
X34 = acov_est34,
X35 = acov_est35,
X36 = acov_est36,
X37 = acov_est37,
X38 = acov_est38,
X39 = acov_est39)
acov_toj <- Rearrangement::rearrangement(x = data.frame(x = acov_x),
y = acov_y)
acov_plot <- ggplot2::ggplot(data.frame(x = acov_x, y = acov_toj),
ggplot2::aes(x = x, y = y)) +
ggplot2::geom_line() +
ggplot2::xlim(min(acov_est), max(acov_est)) +
ggplot2::ylim(0, 1) +
ggplot2::labs(x = "x", y = "") +
ggplot2::ggtitle("The heterogeneous autocovariance") +
ggplot2::theme_bw()
# Autocorrelation
acor_x <- seq(min(acor_est),
max(acor_est),
length = 1000)
acor_y <- tojecdfest1(x = acor_x,
X = acor_est,
X21 = acor_est21,
X22 = acor_est22,
X23 = acor_est23,
X24 = acor_est24,
X31 = acor_est31,
X32 = acor_est32,
X33 = acor_est33,
X34 = acor_est34,
X35 = acor_est35,
X36 = acor_est36,
X37 = acor_est37,
X38 = acor_est38,
X39 = acor_est39)
acor_toj <- Rearrangement::rearrangement(x = data.frame(x = acor_x),
y = acor_y)
acor_plot <- ggplot2::ggplot(data.frame(x = acor_x, y = acor_toj),
ggplot2::aes(x = x, y = y)) +
ggplot2::geom_line() +
ggplot2::xlim(min(acor_est), max(acor_est)) +
ggplot2::ylim(0, 1) +
ggplot2::labs(x = "x", y = "") +
ggplot2::ggtitle("The heterogeneous autocorrelation") +
ggplot2::theme_bw()
}
if (ci) {
# Mean
mean_toj <- cbind(tojecdfest1(x = mean_grid,
X = mean_est,
X21 = mean_est21,
X22 = mean_est22,
X23 = mean_est23,
X24 = mean_est24,
X31 = mean_est31,
X32 = mean_est32,
X33 = mean_est33,
X34 = mean_est34,
X35 = mean_est35,
X36 = mean_est36,
X37 = mean_est37,
X38 = mean_est38,
X39 = mean_est39),
t(mean_ci))
mean_plot <- ggplot2::ggplot(data = data.frame(x = mean_grid),
ggplot2::aes(x = mean_grid)) +
ggplot2::geom_line(
ggplot2::aes(x = mean_grid,
y = Rearrangement::rearrangement(
x = data.frame(x = mean_grid),
y = mean_toj[, 1])
)
) +
ggplot2::geom_ribbon(
ggplot2::aes(x = mean_grid,
ymin = Rearrangement::rearrangement(
x = data.frame(x = mean_grid),
y = mean_toj[, 2]),
ymax = Rearrangement::rearrangement(
x = data.frame(x = mean_grid),
y = mean_toj[, 3])
), alpha = 0.1) +
ggplot2::labs(x = "x", y = "") +
ggplot2::ggtitle("The heterogeneous mean") +
ggplot2::ylim(0, 1) +
ggplot2::theme_bw()
# Autocovariance
acov_toj <- cbind(tojecdfest1(x = acov_grid,
X = acov_est,
X21 = acov_est21,
X22 = acov_est22,
X23 = acov_est23,
X24 = acov_est24,
X31 = acov_est31,
X32 = acov_est32,
X33 = acov_est33,
X34 = acov_est34,
X35 = acov_est35,
X36 = acov_est36,
X37 = acov_est37,
X38 = acov_est38,
X39 = acov_est39),
t(acov_ci))
acov_plot <- ggplot2::ggplot(data = data.frame(x = acov_grid),
ggplot2::aes(x = acov_grid)) +
ggplot2::geom_line(
ggplot2::aes(x = acov_grid,
y = Rearrangement::rearrangement(
x = data.frame(x = acov_grid),
y = acov_toj[, 1])
)
) +
ggplot2::geom_ribbon(
ggplot2::aes(x = acov_grid,
ymin = Rearrangement::rearrangement(
x = data.frame(x = acov_grid),
y = acov_toj[, 2]),
ymax = Rearrangement::rearrangement(
x = data.frame(x = acov_grid),
y = acov_toj[, 3])
), alpha = 0.1) +
ggplot2::labs(x = "x", y = "") +
ggplot2::ggtitle("The heterogeneous autocovariance") +
ggplot2::ylim(0, 1) +
ggplot2::theme_bw()
# Autocorrelation
acor_toj <- cbind(tojecdfest1(x = acor_grid,
X = acor_est,
X21 = acor_est21,
X22 = acor_est22,
X23 = acor_est23,
X24 = acor_est24,
X31 = acor_est31,
X32 = acor_est32,
X33 = acor_est33,
X34 = acor_est34,
X35 = acor_est35,
X36 = acor_est36,
X37 = acor_est37,
X38 = acor_est38,
X39 = acor_est39),
t(acor_ci))
acor_plot <- ggplot2::ggplot(data = data.frame(x = acor_grid),
ggplot2::aes(x = acor_grid)) +
ggplot2::geom_line(
ggplot2::aes(x = acor_grid,
y = Rearrangement::rearrangement(
x = data.frame(x = acor_grid),
y = acor_toj[, 1])
)
) +
ggplot2::geom_ribbon(
ggplot2::aes(x = acor_grid,
ymin = Rearrangement::rearrangement(
x = data.frame(x = acor_grid),
y = acor_toj[, 2]),
ymax = Rearrangement::rearrangement(
x = data.frame(x = acor_grid),
y = acor_toj[, 3])
), alpha = 0.1) +
ggplot2::labs(x = "x", y = "") +
ggplot2::ggtitle("The heterogeneous autocorrelation") +
ggplot2::ylim(0, 1) +
ggplot2::theme_bw()
}
# Functions without rearrangement
mean_func <- function(x) {
tojecdfest1(x = x,
X = mean_est,
X21 = mean_est21,
X22 = mean_est22,
X23 = mean_est23,
X24 = mean_est24,
X31 = mean_est31,
X32 = mean_est32,
X33 = mean_est33,
X34 = mean_est34,
X35 = mean_est35,
X36 = mean_est36,
X37 = mean_est37,
X38 = mean_est38,
X39 = mean_est39)
}
acov_func <- function(x) {
tojecdfest1(x = x,
X = acov_est,
X21 = acov_est21,
X22 = acov_est22,
X23 = acov_est23,
X24 = acov_est24,
X31 = acov_est31,
X32 = acov_est32,
X33 = acov_est33,
X34 = acov_est34,
X35 = acov_est35,
X36 = acov_est36,
X37 = acov_est37,
X38 = acov_est38,
X39 = acov_est39)
}
acor_func <- function(x) {
tojecdfest1(x = x,
X = acor_est,
X21 = acor_est21,
X22 = acor_est22,
X23 = acor_est23,
X24 = acor_est24,
X31 = acor_est31,
X32 = acor_est32,
X33 = acor_est33,
X34 = acor_est34,
X35 = acor_est35,
X36 = acor_est36,
X37 = acor_est37,
X38 = acor_est38,
X39 = acor_est39)
}
} else if (S %% 6 == 2) {
# Split panel data for T equivalent to 2 modulo 6
data21 <- data[, 1:(S / 2)]
data22 <- data[, (S / 2 + 1):S]
data31 <- data[, 1:floor(S / 3)]
data32 <- data[, (floor(S / 3) + 1):(2 * floor(S / 3) + 1) ]
data33 <- data[, (2 * ceiling(S / 3)):S]
data34 <- data[, 1:ceiling(S / 3)]
data35 <- data[, (ceiling(S / 3) + 1):(2 * floor(S / 3) + 1)]
data36 <- data[, (2 * ceiling(S / 3)):S]
data37 <- data[, 1:ceiling(S / 3)]
data38 <- data[, (ceiling(S / 3) + 1):(2 * ceiling(S / 3))]
data39 <- data[, (2 * ceiling(S / 3) + 1):S]
# Estimated quantities for split panel data
mean_est21 <- rowMeans(data21)
mean_est22 <- rowMeans(data22)
mean_est31 <- rowMeans(data31)
mean_est32 <- rowMeans(data32)
mean_est33 <- rowMeans(data33)
mean_est34 <- rowMeans(data34)
mean_est35 <- rowMeans(data35)
mean_est36 <- rowMeans(data36)
mean_est37 <- rowMeans(data37)
mean_est38 <- rowMeans(data38)
mean_est39 <- rowMeans(data39)
acov_est21 <- apply(data21, MARGIN = 1, acov, acov_order = acov_order)
acov_est22 <- apply(data22, MARGIN = 1, acov, acov_order = acov_order)
acov_est31 <- apply(data31, MARGIN = 1, acov, acov_order = acov_order)
acov_est32 <- apply(data32, MARGIN = 1, acov, acov_order = acov_order)
acov_est33 <- apply(data33, MARGIN = 1, acov, acov_order = acov_order)
acov_est34 <- apply(data34, MARGIN = 1, acov, acov_order = acov_order)
acov_est35 <- apply(data35, MARGIN = 1, acov, acov_order = acov_order)
acov_est36 <- apply(data36, MARGIN = 1, acov, acov_order = acov_order)
acov_est37 <- apply(data37, MARGIN = 1, acov, acov_order = acov_order)
acov_est38 <- apply(data38, MARGIN = 1, acov, acov_order = acov_order)
acov_est39 <- apply(data39, MARGIN = 1, acov, acov_order = acov_order)
acor_est21 <- apply(data21, MARGIN = 1, acor, acor_order = acor_order)
acor_est22 <- apply(data22, MARGIN = 1, acor, acor_order = acor_order)
acor_est31 <- apply(data31, MARGIN = 1, acor, acor_order = acor_order)
acor_est32 <- apply(data32, MARGIN = 1, acor, acor_order = acor_order)
acor_est33 <- apply(data33, MARGIN = 1, acor, acor_order = acor_order)
acor_est34 <- apply(data34, MARGIN = 1, acor, acor_order = acor_order)
acor_est35 <- apply(data35, MARGIN = 1, acor, acor_order = acor_order)
acor_est36 <- apply(data36, MARGIN = 1, acor, acor_order = acor_order)
acor_est37 <- apply(data37, MARGIN = 1, acor, acor_order = acor_order)
acor_est38 <- apply(data38, MARGIN = 1, acor, acor_order = acor_order)
acor_est39 <- apply(data39, MARGIN = 1, acor, acor_order = acor_order)
# Function for bootstrap confidence interval
mean_ci_func <- Vectorize(FUN = function(x) {
# TOJ bias-corrected estimation with bootstrap
bootstrap <- boot::boot(data = cbind(mean_est,
mean_est21,
mean_est22,
mean_est31,
mean_est32,
mean_est33,
mean_est34,
mean_est35,
mean_est36,
mean_est37,
mean_est38,
mean_est39) - x,
statistic = toj2_boot,
R = R)
estimate <- bootstrap$t0
temp <- bootstrap$t- bootstrap$t0
# Confidence interval
quantile <- apply(temp,
MARGIN = 2,
stats::quantile,
probs = c(0.025, 0.975))
l_ci <- max(0, estimate + quantile[1])
u_ci <- min(1, estimate + quantile[2])
ci <- cbind(l_ci, u_ci)
colnames(ci) <- c("95% CI lower", "95% CI upper")
return(ci)
}, vectorize.args = "x")
acov_ci_func <- Vectorize(FUN = function(x) {
# TOJ bias-corrected estimation with bootstrap
bootstrap <- boot::boot(data = cbind(acov_est,
acov_est21,
acov_est22,
acov_est31,
acov_est32,
acov_est33,
acov_est34,
acov_est35,
acov_est36,
acov_est37,
acov_est38,
acov_est39) - x,
statistic = toj2_boot,
R = R)
estimate <- bootstrap$t0
temp <- bootstrap$t- bootstrap$t0
# Confidence interval
quantile <- apply(temp,
MARGIN = 2,
stats::quantile,
probs = c(0.025, 0.975))
l_ci <- max(0, estimate + quantile[1])
u_ci <- min(1, estimate + quantile[2])
ci <- cbind(l_ci, u_ci)
colnames(ci) <- c("95% CI lower", "95% CI upper")
return(ci)
}, vectorize.args = "x")
acor_ci_func <- Vectorize(FUN = function(x) {
# TOJ bias-corrected estimation with bootstrap
bootstrap <- boot::boot(data = cbind(acor_est,
acor_est21,
acor_est22,
acor_est31,
acor_est32,
acor_est33,
acor_est34,
acor_est35,
acor_est36,
acor_est37,
acor_est38,
acor_est39) - x,
statistic = toj2_boot,
R = R)
estimate <- bootstrap$t0
temp <- bootstrap$t- bootstrap$t0
# Confidence interval
quantile <- apply(temp,
MARGIN = 2,
stats::quantile,
probs = c(0.025, 0.975))
l_ci <- max(0, estimate + quantile[1])
u_ci <- min(1, estimate + quantile[2])
ci <- cbind(l_ci, u_ci)
colnames(ci) <- c("95% CI lower", "95% CI upper")
return(ci)
}, vectorize.args = "x")
# Limits used for ggplot2
mean_lim <- c(min(mean_est),
max(mean_est))
acov_lim <- c(min(acov_est),
max(acov_est))
acor_lim <- c(min(acor_est),
max(acor_est))
# Compute confidence intervals
if (ci) {
mean_grid <- seq(mean_lim[1], mean_lim[2], length.out = 101)
acov_grid <- seq(acov_lim[1], acov_lim[2], length.out = 101)
acor_grid <- seq(acor_lim[1], acor_lim[2], length.out = 101)
mean_ci <- mean_ci_func(mean_grid)
acov_ci <- acov_ci_func(acov_grid)
acor_ci <- acor_ci_func(acor_grid)
}
# Make figures using ggplot2
if (!ci) {
# Mean
mean_x <- seq(min(mean_est),
max(mean_est),
length = 1000)
mean_y <- tojecdfest2(x = mean_x,
X = mean_est,
X21 = mean_est21,
X22 = mean_est22,
X31 = mean_est31,
X32 = mean_est32,
X33 = mean_est33,
X34 = mean_est34,
X35 = mean_est35,
X36 = mean_est36,
X37 = mean_est37,
X38 = mean_est38,
X39 = mean_est39)
mean_toj <- Rearrangement::rearrangement(x = data.frame(x = mean_x),
y = mean_y)
mean_plot <- ggplot2::ggplot(data.frame(x = mean_x, y = mean_toj),
ggplot2::aes(x = x, y = y)) +
ggplot2::geom_line() +
ggplot2::xlim(min(mean_est), max(mean_est)) +
ggplot2::ylim(0, 1) +
ggplot2::labs(x = "x", y = "") +
ggplot2::ggtitle("The heterogeneous mean") +
ggplot2::theme_bw()
# Autocovariance
acov_x <- seq(min(acov_est),
max(acov_est),
length = 1000)
acov_y <- tojecdfest2(x = acov_x,
X = acov_est,
X21 = acov_est21,
X22 = acov_est22,
X31 = acov_est31,
X32 = acov_est32,
X33 = acov_est33,
X34 = acov_est34,
X35 = acov_est35,
X36 = acov_est36,
X37 = acov_est37,
X38 = acov_est38,
X39 = acov_est39)
acov_toj <- Rearrangement::rearrangement(x = data.frame(x = acov_x),
y = acov_y)
acov_plot <- ggplot2::ggplot(data.frame(x = acov_x, y = acov_toj),
ggplot2::aes(x = x, y = y)) +
ggplot2::geom_line() +
ggplot2::xlim(min(acov_est), max(acov_est)) +
ggplot2::ylim(0, 1) +
ggplot2::labs(x = "x", y = "") +
ggplot2::ggtitle("The heterogeneous autocovariance") +
ggplot2::theme_bw()
# Autocorrelation
acor_x <- seq(min(acor_est),
max(acor_est),
length = 1000)
acor_y <- tojecdfest2(x = acor_x,
X = acor_est,
X21 = acor_est21,
X22 = acor_est22,
X31 = acor_est31,
X32 = acor_est32,
X33 = acor_est33,
X34 = acor_est34,
X35 = acor_est35,
X36 = acor_est36,
X37 = acor_est37,
X38 = acor_est38,
X39 = acor_est39)
acor_toj <- Rearrangement::rearrangement(x = data.frame(x = acor_x),
y = acor_y)
acor_plot <- ggplot2::ggplot(data.frame(x = acor_x, y = acor_toj),
ggplot2::aes(x = x, y = y)) +
ggplot2::geom_line() +
ggplot2::xlim(min(acor_est), max(acor_est)) +
ggplot2::ylim(0, 1) +
ggplot2::labs(x = "x", y = "") +
ggplot2::ggtitle("The heterogeneous autocorrelation") +
ggplot2::theme_bw()
}
if (ci) {
# Mean
mean_toj <- cbind(tojecdfest2(x = mean_grid,
X = mean_est,
X21 = mean_est21,
X22 = mean_est22,
X31 = mean_est31,
X32 = mean_est32,
X33 = mean_est33,
X34 = mean_est34,
X35 = mean_est35,
X36 = mean_est36,
X37 = mean_est37,
X38 = mean_est38,
X39 = mean_est39),
t(mean_ci))
mean_plot <- ggplot2::ggplot(data = data.frame(x = mean_grid),
ggplot2::aes(x = mean_grid)) +
ggplot2::geom_line(
ggplot2::aes(x = mean_grid,
y = Rearrangement::rearrangement(
x = data.frame(x = mean_grid),
y = mean_toj[, 1])
)
) +
ggplot2::geom_ribbon(
ggplot2::aes(x = mean_grid,
ymin = Rearrangement::rearrangement(
x = data.frame(x = mean_grid),
y = mean_toj[, 2]),
ymax = Rearrangement::rearrangement(
x = data.frame(x = mean_grid),
y = mean_toj[, 3])
),
alpha = 0.1) +
ggplot2::labs(x = "x", y = "") +
ggplot2::ggtitle("The heterogeneous mean") +
ggplot2::ylim(0, 1) +
ggplot2::theme_bw()
# Autocovariance
acov_toj <- cbind(tojecdfest2(x = acov_grid,
X = acov_est,
X21 = acov_est21,
X22 = acov_est22,
X31 = acov_est31,
X32 = acov_est32,
X33 = acov_est33,
X34 = acov_est34,
X35 = acov_est35,
X36 = acov_est36,
X37 = acov_est37,
X38 = acov_est38,
X39 = acov_est39),
t(acov_ci))
acov_plot <- ggplot2::ggplot(data = data.frame(x = acov_grid),
ggplot2::aes(x = acov_grid)) +
ggplot2::geom_line(
ggplot2::aes(x = acov_grid,
y = Rearrangement::rearrangement(
x = data.frame(x = acov_grid),
y = acov_toj[, 1])
)
) +
ggplot2::geom_ribbon(
ggplot2::aes(x = acov_grid,
ymin = Rearrangement::rearrangement(
x = data.frame(x = acov_grid),
y = acov_toj[, 2]),
ymax = Rearrangement::rearrangement(
x = data.frame(x = acov_grid),
y = acov_toj[, 3])
),
alpha = 0.1) +
ggplot2::labs(x = "x", y = "") +
ggplot2::ggtitle("The heterogeneous autocovariance") +
ggplot2::ylim(0, 1) +
ggplot2::theme_bw()
# Autocorrelation
acor_toj <- cbind(tojecdfest2(x = acor_grid,
X = acor_est,
X21 = acor_est21,
X22 = acor_est22,
X31 = acor_est31,
X32 = acor_est32,
X33 = acor_est33,
X34 = acor_est34,
X35 = acor_est35,
X36 = acor_est36,
X37 = acor_est37,
X38 = acor_est38,
X39 = acor_est39),
t(acor_ci))
acor_plot <- ggplot2::ggplot(data = data.frame(x = acor_grid),
ggplot2::aes(x = acor_grid)) +
ggplot2::geom_line(
ggplot2::aes(x = acor_grid,
y = Rearrangement::rearrangement(
x = data.frame(x = acor_grid),
y = acor_toj[, 1])
)
) +
ggplot2::geom_ribbon(
ggplot2::aes(x = acor_grid,
ymin = Rearrangement::rearrangement(
x = data.frame(x = acor_grid),
y = acor_toj[, 2]),
ymax = Rearrangement::rearrangement(
x = data.frame(x = acor_grid),
y = acor_toj[, 3])
),
alpha = 0.1) +
ggplot2::labs(x = "x", y = "") +
ggplot2::ggtitle("The heterogeneous autocorrelation") +
ggplot2::ylim(0, 1) +
ggplot2::theme_bw()
}
# Functions without rearrangement
mean_func <- function(x) {
tojecdfest2(x = x,
X = mean_est,
X21 = mean_est21,
X22 = mean_est22,
X31 = mean_est31,
X32 = mean_est32,
X33 = mean_est33,
X34 = mean_est34,
X35 = mean_est35,
X36 = mean_est36,
X37 = mean_est37,
X38 = mean_est38,
X39 = mean_est39)
}
acov_func <- function(x) {
tojecdfest2(x = x,
X = acov_est,
X21 = acov_est21,
X22 = acov_est22,
X31 = acov_est31,
X32 = acov_est32,
X33 = acov_est33,
X34 = acov_est34,
X35 = acov_est35,
X36 = acov_est36,
X37 = acov_est37,
X38 = acov_est38,
X39 = acov_est39)
}
acor_func <- function(x) {
tojecdfest2(x = x,
X = acor_est,
X21 = acor_est21,
X22 = acor_est22,
X31 = acor_est31,
X32 = acor_est32,
X33 = acor_est33,
X34 = acor_est34,
X35 = acor_est35,
X36 = acor_est36,
X37 = acor_est37,
X38 = acor_est38,
X39 = acor_est39)
}
} else if (S %% 6 == 3) {
# Split panel data for T equivalent to 3 modulo 6
data21 <- data[, 1:floor(S / 2)]
data22 <- data[, (floor(S / 2) + 1):S]
data23 <- data[, 1:ceiling(S / 2)]
data24 <- data[, (ceiling(S / 2) + 1):S]
data31 <- data[, 1:(S / 3)]
data32 <- data[, (S / 3 + 1):(2*S / 3)]
data33 <- data[, (2 * S / 3 + 1):S]
# Estimated quantities for split panel data
mean_est21 <- rowMeans(data21)
mean_est22 <- rowMeans(data22)
mean_est23 <- rowMeans(data23)
mean_est24 <- rowMeans(data24)
mean_est31 <- rowMeans(data31)
mean_est32 <- rowMeans(data32)
mean_est33 <- rowMeans(data33)
acov_est21 <- apply(data21, MARGIN = 1, acov, acov_order = acov_order)
acov_est22 <- apply(data22, MARGIN = 1, acov, acov_order = acov_order)
acov_est23 <- apply(data23, MARGIN = 1, acov, acov_order = acov_order)
acov_est24 <- apply(data24, MARGIN = 1, acov, acov_order = acov_order)
acov_est31 <- apply(data31, MARGIN = 1, acov, acov_order = acov_order)
acov_est32 <- apply(data32, MARGIN = 1, acov, acov_order = acov_order)
acov_est33 <- apply(data33, MARGIN = 1, acov, acov_order = acov_order)
acor_est21 <- apply(data21, MARGIN = 1, acor, acor_order = acor_order)
acor_est22 <- apply(data22, MARGIN = 1, acor, acor_order = acor_order)
acor_est23 <- apply(data23, MARGIN = 1, acor, acor_order = acor_order)
acor_est24 <- apply(data24, MARGIN = 1, acor, acor_order = acor_order)
acor_est31 <- apply(data31, MARGIN = 1, acor, acor_order = acor_order)
acor_est32 <- apply(data32, MARGIN = 1, acor, acor_order = acor_order)
acor_est33 <- apply(data33, MARGIN = 1, acor, acor_order = acor_order)
# Function for bootstrap confidence interval
mean_ci_func <- Vectorize(FUN = function(x) {
# TOJ bias-corrected estimation with bootstrap
bootstrap <- boot::boot(data = cbind(mean_est,
mean_est21,
mean_est22,
mean_est23,
mean_est24,
mean_est31,
mean_est32,
mean_est33) - x,
statistic = toj3_boot,
R = R)
estimate <- bootstrap$t0
temp <- bootstrap$t- bootstrap$t0
# Confidence interval
quantile <- apply(temp,
MARGIN = 2,
stats::quantile,
probs = c(0.025, 0.975))
l_ci <- max(0, estimate + quantile[1])
u_ci <- min(1, estimate + quantile[2])
ci <- cbind(l_ci, u_ci)
colnames(ci) <- c("95% CI lower", "95% CI upper")
return(ci)
}, vectorize.args = "x")
acov_ci_func <- Vectorize(FUN = function(x) {
# TOJ bias-corrected estimation with bootstrap
bootstrap <- boot::boot(data = cbind(acov_est,
acov_est21,
acov_est22,
acov_est23,
acov_est24,
acov_est31,
acov_est32,
acov_est33) - x,
statistic = toj3_boot,
R = R)
estimate <- bootstrap$t0
temp <- bootstrap$t- bootstrap$t0
# Confidence interval
quantile <- apply(temp,
MARGIN = 2,
stats::quantile,
probs = c(0.025, 0.975))
l_ci <- max(0, estimate + quantile[1])
u_ci <- min(1, estimate + quantile[2])
ci <- cbind(l_ci, u_ci)
colnames(ci) <- c("95% CI lower", "95% CI upper")
return(ci)
}, vectorize.args = "x")
acor_ci_func <- Vectorize(FUN = function(x) {
# TOJ bias-corrected estimation with bootstrap
bootstrap <- boot::boot(data = cbind(acor_est,
acor_est21,
acor_est22,
acor_est23,
acor_est24,
acor_est31,
acor_est32,
acor_est33) - x,
statistic = toj3_boot,
R = R)
estimate <- bootstrap$t0
temp <- bootstrap$t- bootstrap$t0
# Confidence interval
quantile <- apply(temp,
MARGIN = 2,
stats::quantile,
probs = c(0.025, 0.975))
l_ci <- max(0, estimate + quantile[1])
u_ci <- min(1, estimate + quantile[2])
ci <- cbind(l_ci, u_ci)
colnames(ci) <- c("95% CI lower", "95% CI upper")
return(ci)
}, vectorize.args = "x")
# Limits used for ggplot2
mean_lim <- c(min(mean_est),
max(mean_est))
acov_lim <- c(min(acov_est),
max(acov_est))
acor_lim <- c(min(acor_est),
max(acor_est))
# Compute confidence intervals
if (ci) {
mean_grid <- seq(mean_lim[1], mean_lim[2], length.out = 101)
acov_grid <- seq(acov_lim[1], acov_lim[2], length.out = 101)
acor_grid <- seq(acor_lim[1], acor_lim[2], length.out = 101)
mean_ci <- mean_ci_func(mean_grid)
acov_ci <- acov_ci_func(acov_grid)
acor_ci <- acor_ci_func(acor_grid)
}
# Make figures using ggplot2
if (!ci) {
# Mean
mean_x <- seq(min(mean_est),
max(mean_est),
length = 1000)
mean_y <- tojecdfest3(x = mean_x,
X = mean_est,
X21 = mean_est21,
X22 = mean_est22,
X23 = mean_est23,
X24 = mean_est24,
X31 = mean_est31,
X32 = mean_est32,
X33 = mean_est33)
mean_toj <- Rearrangement::rearrangement(x = data.frame(x = mean_x),
y = mean_y)
mean_plot <- ggplot2::ggplot(data.frame(x = mean_x, y = mean_toj),
ggplot2::aes(x = x, y = y)) +
ggplot2::geom_line() +
ggplot2::xlim(min(mean_est), max(mean_est)) +
ggplot2::ylim(0, 1) +
ggplot2::labs(x = "x", y = "") +
ggplot2::ggtitle("The heterogeneous mean") +
ggplot2::theme_bw()
# Autocovariance
acov_x <- seq(min(acov_est),
max(acov_est),
length = 1000)
acov_y <- tojecdfest3(x = acov_x,
X = acov_est,
X21 = acov_est21,
X22 = acov_est22,
X23 = acov_est23,
X24 = acov_est24,
X31 = acov_est31,
X32 = acov_est32,
X33 = acov_est33)
acov_toj <- Rearrangement::rearrangement(x = data.frame(x = acov_x),
y = acov_y)
acov_plot <- ggplot2::ggplot(data.frame(x = acov_x, y = acov_toj),
ggplot2::aes(x = x, y = y)) +
ggplot2::geom_line() +
ggplot2::xlim(min(acov_est), max(acov_est)) +
ggplot2::ylim(0, 1) +
ggplot2::labs(x = "x", y = "") +
ggplot2::ggtitle("The heterogeneous autocovariance") +
ggplot2::theme_bw()
# Autocorrelation
acor_x <- seq(min(acor_est),
max(acor_est),
length = 1000)
acor_y <- tojecdfest3(x = acor_x,
X = acor_est,
X21 = acor_est21,
X22 = acor_est22,
X23 = acor_est23,
X24 = acor_est24,
X31 = acor_est31,
X32 = acor_est32,
X33 = acor_est33)
acor_toj <- Rearrangement::rearrangement(x = data.frame(x = acor_x),
y = acor_y)
acor_plot <- ggplot2::ggplot(data.frame(x = acor_x, y = acor_toj),
ggplot2::aes(x = x, y = y)) +
ggplot2::geom_line() +
ggplot2::xlim(min(acor_est), max(acor_est)) +
ggplot2::ylim(0, 1) +
ggplot2::labs(x = "x", y = "") +
ggplot2::ggtitle("The heterogeneous autocorrelation") +
ggplot2::theme_bw()
}
if (ci) {
# Mean
mean_toj <- cbind(tojecdfest3(x = mean_grid,
X = mean_est,
X21 = mean_est21,
X22 = mean_est22,
X23 = mean_est23,
X24 = mean_est24,
X31 = mean_est31,
X32 = mean_est32,
X33 = mean_est33),
t(mean_ci))
mean_plot <- ggplot2::ggplot(data = data.frame(x = mean_grid),
ggplot2::aes(x = mean_grid)) +
ggplot2::geom_line(
ggplot2::aes(x = mean_grid,
y = Rearrangement::rearrangement(
x = data.frame(x = mean_grid),
y = mean_toj[, 1])
)
) +
ggplot2::geom_ribbon(
ggplot2::aes(
x = mean_grid,
ymin = Rearrangement::rearrangement(
x = data.frame(x = mean_grid),
y = mean_toj[, 2]),
ymax = Rearrangement::rearrangement(
x = data.frame(x = mean_grid),
y = mean_toj[, 3])
),
alpha = 0.1) +
ggplot2::labs(x = "x", y = "") +
ggplot2::ggtitle("The heterogeneous mean") +
ggplot2::ylim(0, 1) +
ggplot2::theme_bw()
# Autocovariance
acov_toj <- cbind(tojecdfest3(x = acov_grid,
X = acov_est,
X21 = acov_est21,
X22 = acov_est22,
X23 = acov_est23,
X24 = acov_est24,
X31 = acov_est31,
X32 = acov_est32,
X33 = acov_est33),
t(acov_ci))
acov_plot <- ggplot2::ggplot(data = data.frame(x = acov_grid),
ggplot2::aes(x = acov_grid)) +
ggplot2::geom_line(
ggplot2::aes(x = acov_grid,
y = Rearrangement::rearrangement(
x = data.frame(x = acov_grid),
y = acov_toj[, 1])
)
) +
ggplot2::geom_ribbon(
ggplot2::aes(
x = acov_grid,
ymin = Rearrangement::rearrangement(
x = data.frame(x = acov_grid),
y = acov_toj[, 2]),
ymax = Rearrangement::rearrangement(
x = data.frame(x = acov_grid),
y = acov_toj[, 3])
),
alpha = 0.1) +
ggplot2::labs(x = "x", y = "") +
ggplot2::ggtitle("The heterogeneous autocovariance") +
ggplot2::ylim(0, 1) +
ggplot2::theme_bw()
# Autocorrelation
acor_toj <- cbind(tojecdfest3(x = acor_grid,
X = acor_est,
X21 = acor_est21,
X22 = acor_est22,
X23 = acor_est23,
X24 = acor_est24,
X31 = acor_est31,
X32 = acor_est32,
X33 = acor_est33),
t(acor_ci))
acor_plot <- ggplot2::ggplot(data = data.frame(x = acor_grid),
ggplot2::aes(x = acor_grid)) +
ggplot2::geom_line(
ggplot2::aes(x = acor_grid,
y = Rearrangement::rearrangement(
x = data.frame(x = acor_grid),
y = acor_toj[, 1])
)
) +
ggplot2::geom_ribbon(
ggplot2::aes(
x = acor_grid,
ymin = Rearrangement::rearrangement(
x = data.frame(x = acor_grid),
y = acor_toj[, 2]),
ymax = Rearrangement::rearrangement(
x = data.frame(x = acor_grid),
y = acor_toj[, 3])
),
alpha = 0.1) +
ggplot2::labs(x = "x", y = "") +
ggplot2::ggtitle("The heterogeneous autocorrelation") +
ggplot2::ylim(0, 1) +
ggplot2::theme_bw()
}
# Functions without rearrangement
mean_func <- function(x) {
tojecdfest3(x = x,
X = mean_est,
X21 = mean_est21,
X22 = mean_est22,
X23 = mean_est23,
X24 = mean_est24,
X31 = mean_est31,
X32 = mean_est32,
X33 = mean_est33)
}
acov_func <- function(x) {
tojecdfest3(x = x,
X = acov_est,
X21 = acov_est21,
X22 = acov_est22,
X23 = acov_est23,
X24 = acov_est24,
X31 = acov_est31,
X32 = acov_est32,
X33 = acov_est33)
}
acor_func <- function(x) {
tojecdfest3(x = x,
X = acor_est,
X21 = acor_est21,
X22 = acor_est22,
X23 = acor_est23,
X24 = acor_est24,
X31 = acor_est31,
X32 = acor_est32,
X33 = acor_est33)
}
} else if (S %% 6 == 4) {
# Split panel data for T equivalent to 4 modulo 6
data21 <- data[, 1:(S / 2)]
data22 <- data[, (S / 2 + 1):S]
data31 <- data[, 1:floor(S / 3)]
data32 <- data[, (floor(S / 3) + 1):(2 * floor(S / 3))]
data33 <- data[, (2 * floor(S / 3) + 1):S]
data34 <- data[, 1:floor(S / 3)]
data35 <- data[, (floor(S / 3) + 1):(2 * floor(S / 3) + 1)]
data36 <- data[, (2 * floor(S / 3) + 2):S]
data37 <- data[, 1:ceiling(S / 3)]
data38 <- data[, (ceiling(S / 3) + 1):(2 * floor(S / 3) + 1)]
data39 <- data[, (2 * floor(S / 3) + 2):S]
# Estimated quantities for split panel data
mean_est21 <- rowMeans(data21)
mean_est22 <- rowMeans(data22)
mean_est31 <- rowMeans(data31)
mean_est32 <- rowMeans(data32)
mean_est33 <- rowMeans(data33)
mean_est34 <- rowMeans(data34)
mean_est35 <- rowMeans(data35)
mean_est36 <- rowMeans(data36)
mean_est37 <- rowMeans(data37)
mean_est38 <- rowMeans(data38)
mean_est39 <- rowMeans(data39)
acov_est21 <- apply(data21, MARGIN = 1, acov, acov_order = acov_order)
acov_est22 <- apply(data22, MARGIN = 1, acov, acov_order = acov_order)
acov_est31 <- apply(data31, MARGIN = 1, acov, acov_order = acov_order)
acov_est32 <- apply(data32, MARGIN = 1, acov, acov_order = acov_order)
acov_est33 <- apply(data33, MARGIN = 1, acov, acov_order = acov_order)
acov_est34 <- apply(data34, MARGIN = 1, acov, acov_order = acov_order)
acov_est35 <- apply(data35, MARGIN = 1, acov, acov_order = acov_order)
acov_est36 <- apply(data36, MARGIN = 1, acov, acov_order = acov_order)
acov_est37 <- apply(data37, MARGIN = 1, acov, acov_order = acov_order)
acov_est38 <- apply(data38, MARGIN = 1, acov, acov_order = acov_order)
acov_est39 <- apply(data39, MARGIN = 1, acov, acov_order = acov_order)
acor_est21 <- apply(data21, MARGIN = 1, acor, acor_order = acor_order)
acor_est22 <- apply(data22, MARGIN = 1, acor, acor_order = acor_order)
acor_est31 <- apply(data31, MARGIN = 1, acor, acor_order = acor_order)
acor_est32 <- apply(data32, MARGIN = 1, acor, acor_order = acor_order)
acor_est33 <- apply(data33, MARGIN = 1, acor, acor_order = acor_order)
acor_est34 <- apply(data34, MARGIN = 1, acor, acor_order = acor_order)
acor_est35 <- apply(data35, MARGIN = 1, acor, acor_order = acor_order)
acor_est36 <- apply(data36, MARGIN = 1, acor, acor_order = acor_order)
acor_est37 <- apply(data37, MARGIN = 1, acor, acor_order = acor_order)
acor_est38 <- apply(data38, MARGIN = 1, acor, acor_order = acor_order)
acor_est39 <- apply(data39, MARGIN = 1, acor, acor_order = acor_order)
# Function for bootstrap confidence interval
mean_ci_func <- Vectorize(FUN = function(x) {
# TOJ bias-corrected estimation with bootstrap
bootstrap <- boot::boot(data = cbind(mean_est,
mean_est21,
mean_est22,
mean_est31,
mean_est32,
mean_est33,
mean_est34,
mean_est35,
mean_est36,
mean_est37,
mean_est38,
mean_est39) - x,
statistic = toj4_boot,
R = R)
estimate <- bootstrap$t0
temp <- bootstrap$t- bootstrap$t0
# Confidence interval
quantile <- apply(temp,
MARGIN = 2,
stats::quantile,
probs = c(0.025, 0.975))
l_ci <- max(0, estimate + quantile[1])
u_ci <- min(1, estimate + quantile[2])
ci <- cbind(l_ci, u_ci)
colnames(ci) <- c("95% CI lower", "95% CI upper")
return(ci)
}, vectorize.args = "x")
acov_ci_func <- Vectorize(FUN = function(x) {
# TOJ bias-corrected estimation with bootstrap
bootstrap <- boot::boot(data = cbind(acov_est,
acov_est21,
acov_est22,
acov_est31,
acov_est32,
acov_est33,
acov_est34,
acov_est35,
acov_est36,
acov_est37,
acov_est38,
acov_est39) - x,
statistic = toj4_boot,
R = R)
estimate <- bootstrap$t0
temp <- bootstrap$t- bootstrap$t0
# Confidence interval
quantile <- apply(temp,
MARGIN = 2,
stats::quantile,
probs = c(0.025, 0.975))
l_ci <- max(0, estimate + quantile[1])
u_ci <- min(1, estimate + quantile[2])
ci <- cbind(l_ci, u_ci)
colnames(ci) <- c("95% CI lower", "95% CI upper")
return(ci)
}, vectorize.args = "x")
acor_ci_func <- Vectorize(FUN = function(x) {
# TOJ bias-corrected estimation with bootstrap
bootstrap <- boot::boot(data = cbind(acor_est,
acor_est21,
acor_est22,
acor_est31,
acor_est32,
acor_est33,
acor_est34,
acor_est35,
acor_est36,
acor_est37,
acor_est38,
acor_est39) - x,
statistic = toj4_boot,
R = R)
estimate <- bootstrap$t0
temp <- bootstrap$t- bootstrap$t0
# Confidence interval
quantile <- apply(temp,
MARGIN = 2,
stats::quantile,
probs = c(0.025, 0.975))
l_ci <- max(0, estimate + quantile[1])
u_ci <- min(1, estimate + quantile[2])
ci <- cbind(l_ci, u_ci)
colnames(ci) <- c("95% CI lower", "95% CI upper")
return(ci)
}, vectorize.args = "x")
# Limits used for ggplot2
mean_lim <- c(min(mean_est),
max(mean_est))
acov_lim <- c(min(acov_est),
max(acov_est))
acor_lim <- c(min(acor_est),
max(acor_est))
# Compute confidence intervals
if (ci) {
mean_grid <- seq(mean_lim[1], mean_lim[2], length.out = 101)
acov_grid <- seq(acov_lim[1], acov_lim[2], length.out = 101)
acor_grid <- seq(acor_lim[1], acor_lim[2], length.out = 101)
mean_ci <- mean_ci_func(mean_grid)
acov_ci <- acov_ci_func(acov_grid)
acor_ci <- acor_ci_func(acor_grid)
}
# Make figures using ggplot2
if (!ci) {
# Mean
mean_x <- seq(min(mean_est),
max(mean_est),
length = 1000)
mean_y <- tojecdfest4(x = mean_x,
X = mean_est,
X21 = mean_est21,
X22 = mean_est22,
X31 = mean_est31,
X32 = mean_est32,
X33 = mean_est33,
X34 = mean_est34,
X35 = mean_est35,
X36 = mean_est36,
X37 = mean_est37,
X38 = mean_est38,
X39 = mean_est39)
mean_toj <- Rearrangement::rearrangement(x = data.frame(x = mean_x),
y = mean_y)
mean_plot <- ggplot2::ggplot(data.frame(x = mean_x, y = mean_toj),
ggplot2::aes(x = x, y = y)) +
ggplot2::geom_line() +
ggplot2::xlim(min(mean_est), max(mean_est)) +
ggplot2::ylim(0, 1) +
ggplot2::labs(x = "x", y = "") +
ggplot2::ggtitle("The heterogeneous mean") +
ggplot2::theme_bw()
# Autocovariance
acov_x <- seq(min(acov_est),
max(acov_est),
length = 1000)
acov_y <- tojecdfest4(x = acov_x,
X = acov_est,
X21 = acov_est21,
X22 = acov_est22,
X31 = acov_est31,
X32 = acov_est32,
X33 = acov_est33,
X34 = acov_est34,
X35 = acov_est35,
X36 = acov_est36,
X37 = acov_est37,
X38 = acov_est38,
X39 = acov_est39)
acov_toj <- Rearrangement::rearrangement(x = data.frame(x = acov_x),
y = acov_y)
acov_plot <- ggplot2::ggplot(data.frame(x = acov_x, y = acov_toj),
ggplot2::aes(x = x, y = y)) +
ggplot2::geom_line() +
ggplot2::xlim(min(acov_est), max(acov_est)) +
ggplot2::ylim(0, 1) +
ggplot2::labs(x = "x", y = "") +
ggplot2::ggtitle("The heterogeneous autocovariance") +
ggplot2::theme_bw()
# Autocorrelation
acor_x <- seq(min(acor_est),
max(acor_est),
length = 1000)
acor_y <- tojecdfest4(x = acor_x,
X = acor_est,
X21 = acor_est21,
X22 = acor_est22,
X31 = acor_est31,
X32 = acor_est32,
X33 = acor_est33,
X34 = acor_est34,
X35 = acor_est35,
X36 = acor_est36,
X37 = acor_est37,
X38 = acor_est38,
X39 = acor_est39)
acor_toj <- Rearrangement::rearrangement(x = data.frame(x = acor_x),
y = acor_y)
acor_plot <- ggplot2::ggplot(data.frame(x = acor_x, y = acor_toj),
ggplot2::aes(x = x, y = y)) +
ggplot2::geom_line() +
ggplot2::xlim(min(acor_est), max(acor_est)) +
ggplot2::ylim(0, 1) +
ggplot2::labs(x = "x", y = "") +
ggplot2::ggtitle("The heterogeneous autocorrelation") +
ggplot2::theme_bw()
}
if (ci) {
# Mean
mean_toj <- cbind(tojecdfest4(x = mean_grid,
X = mean_est,
X21 = mean_est21,
X22 = mean_est22,
X31 = mean_est31,
X32 = mean_est32,
X33 = mean_est33,
X34 = mean_est34,
X35 = mean_est35,
X36 = mean_est36,
X37 = mean_est37,
X38 = mean_est38,
X39 = mean_est39),
t(mean_ci))
mean_plot <- ggplot2::ggplot(data = data.frame(x = mean_grid),
ggplot2::aes(x = mean_grid)) +
ggplot2::geom_line(
ggplot2::aes(
x = mean_grid,
y = Rearrangement::rearrangement(
x = data.frame(x = mean_grid),
y = mean_toj[, 1])
)
) +
ggplot2::geom_ribbon(
ggplot2::aes(
x = mean_grid,
ymin = Rearrangement::rearrangement(
x = data.frame(x = mean_grid),
y = mean_toj[, 2]),
ymax = Rearrangement::rearrangement(
x = data.frame(x = mean_grid),
y = mean_toj[, 3])
),
alpha = 0.1) +
ggplot2::labs(x = "x", y = "") +
ggplot2::ggtitle("The heterogeneous mean") +
ggplot2::ylim(0, 1) +
ggplot2::theme_bw()
# Autocovariance
acov_toj <- cbind(tojecdfest4(x = acov_grid,
X = acov_est,
X21 = acov_est21,
X22 = acov_est22,
X31 = acov_est31,
X32 = acov_est32,
X33 = acov_est33,
X34 = acov_est34,
X35 = acov_est35,
X36 = acov_est36,
X37 = acov_est37,
X38 = acov_est38,
X39 = acov_est39),
t(acov_ci))
acov_plot <- ggplot2::ggplot(data = data.frame(x = acov_grid),
ggplot2::aes(x = acov_grid)) +
ggplot2::geom_line(
ggplot2::aes(
x = acov_grid,
y = Rearrangement::rearrangement(
x = data.frame(x = acov_grid),
y = acov_toj[, 1])
)
) +
ggplot2::geom_ribbon(
ggplot2::aes(
x = acov_grid,
ymin = Rearrangement::rearrangement(
x = data.frame(x = acov_grid),
y = acov_toj[, 2]),
ymax = Rearrangement::rearrangement(
x = data.frame(x = acov_grid),
y = acov_toj[, 3])
),
alpha = 0.1) +
ggplot2::labs(x = "x", y = "") +
ggplot2::ggtitle("The heterogeneous autocovariance") +
ggplot2::ylim(0, 1) +
ggplot2::theme_bw()
# Autocorrelation
acor_toj <- cbind(tojecdfest4(x = acor_grid,
X = acor_est,
X21 = acor_est21,
X22 = acor_est22,
X31 = acor_est31,
X32 = acor_est32,
X33 = acor_est33,
X34 = acor_est34,
X35 = acor_est35,
X36 = acor_est36,
X37 = acor_est37,
X38 = acor_est38,
X39 = acor_est39),
t(acor_ci))
acor_plot <- ggplot2::ggplot(data = data.frame(x = acor_grid),
ggplot2::aes(x = acor_grid)) +
ggplot2::geom_line(
ggplot2::aes(
x = acor_grid,
y = Rearrangement::rearrangement(
x = data.frame(x = acor_grid),
y = acor_toj[, 1])
)
) +
ggplot2::geom_ribbon(
ggplot2::aes(
x = acor_grid,
ymin = Rearrangement::rearrangement(
x = data.frame(x = acor_grid),
y = acor_toj[, 2]),
ymax = Rearrangement::rearrangement(
x = data.frame(x = acor_grid),
y = acor_toj[, 3])
),
alpha = 0.1) +
ggplot2::labs(x = "x", y = "") +
ggplot2::ggtitle("The heterogeneous autocorrelation") +
ggplot2::ylim(0, 1) +
ggplot2::theme_bw()
}
# Functions without rearrangement
mean_func <- function(x) {
tojecdfest4(x = x,
X = mean_est,
X21 = mean_est21,
X22 = mean_est22,
X31 = mean_est31,
X32 = mean_est32,
X33 = mean_est33,
X34 = mean_est34,
X35 = mean_est35,
X36 = mean_est36,
X37 = mean_est37,
X38 = mean_est38,
X39 = mean_est39)
}
acov_func <- function(x) {
tojecdfest4(x = x,
X = acov_est,
X21 = acov_est21,
X22 = acov_est22,
X31 = acov_est31,
X32 = acov_est32,
X33 = acov_est33,
X34 = acov_est34,
X35 = acov_est35,
X36 = acov_est36,
X37 = acov_est37,
X38 = acov_est38,
X39 = acov_est39)
}
acor_func <- function(x) {
tojecdfest4(x = x,
X = acor_est,
X21 = acor_est21,
X22 = acor_est22,
X31 = acor_est31,
X32 = acor_est32,
X33 = acor_est33,
X34 = acor_est34,
X35 = acor_est35,
X36 = acor_est36,
X37 = acor_est37,
X38 = acor_est38,
X39 = acor_est39)
}
} else {
# Split panel data for T equivalent to 5 modulo 6
data21 <- data[, 1:floor(S / 2)]
data22 <- data[, (floor(S / 2) + 1):S]
data23 <- data[, 1:ceiling(S / 2)]
data24 <- data[, (ceiling(S / 2) + 1):S]
data31 <- data[, 1:floor(S / 3)]
data32 <- data[, (floor(S / 3) + 1):(2 * floor(S / 3) + 1) ]
data33 <- data[, (2 * ceiling(S / 3)):S]
data34 <- data[, 1:ceiling(S / 3)]
data35 <- data[, (ceiling(S / 3) + 1):(2 * floor(S / 3) + 1)]
data36 <- data[, (2 * ceiling(S / 3)):S]
data37 <- data[, 1:ceiling(S / 3)]
data38 <- data[, (ceiling(S / 3) + 1):(2 * ceiling(S / 3))]
data39 <- data[, (2 * ceiling(S / 3) + 1):S]
# Estimated quantities for split panel data
mean_est21 <- rowMeans(data21)
mean_est22 <- rowMeans(data22)
mean_est23 <- rowMeans(data23)
mean_est24 <- rowMeans(data24)
mean_est31 <- rowMeans(data31)
mean_est32 <- rowMeans(data32)
mean_est33 <- rowMeans(data33)
mean_est34 <- rowMeans(data34)
mean_est35 <- rowMeans(data35)
mean_est36 <- rowMeans(data36)
mean_est37 <- rowMeans(data37)
mean_est38 <- rowMeans(data38)
mean_est39 <- rowMeans(data39)
acov_est21 <- apply(data21, MARGIN = 1, acov, acov_order = acov_order)
acov_est22 <- apply(data22, MARGIN = 1, acov, acov_order = acov_order)
acov_est23 <- apply(data23, MARGIN = 1, acov, acov_order = acov_order)
acov_est24 <- apply(data24, MARGIN = 1, acov, acov_order = acov_order)
acov_est31 <- apply(data31, MARGIN = 1, acov, acov_order = acov_order)
acov_est32 <- apply(data32, MARGIN = 1, acov, acov_order = acov_order)
acov_est33 <- apply(data33, MARGIN = 1, acov, acov_order = acov_order)
acov_est34 <- apply(data34, MARGIN = 1, acov, acov_order = acov_order)
acov_est35 <- apply(data35, MARGIN = 1, acov, acov_order = acov_order)
acov_est36 <- apply(data36, MARGIN = 1, acov, acov_order = acov_order)
acov_est37 <- apply(data37, MARGIN = 1, acov, acov_order = acov_order)
acov_est38 <- apply(data38, MARGIN = 1, acov, acov_order = acov_order)
acov_est39 <- apply(data39, MARGIN = 1, acov, acov_order = acov_order)
acor_est21 <- apply(data21, MARGIN = 1, acor, acor_order = acor_order)
acor_est22 <- apply(data22, MARGIN = 1, acor, acor_order = acor_order)
acor_est23 <- apply(data23, MARGIN = 1, acor, acor_order = acor_order)
acor_est24 <- apply(data24, MARGIN = 1, acor, acor_order = acor_order)
acor_est31 <- apply(data31, MARGIN = 1, acor, acor_order = acor_order)
acor_est32 <- apply(data32, MARGIN = 1, acor, acor_order = acor_order)
acor_est33 <- apply(data33, MARGIN = 1, acor, acor_order = acor_order)
acor_est34 <- apply(data34, MARGIN = 1, acor, acor_order = acor_order)
acor_est35 <- apply(data35, MARGIN = 1, acor, acor_order = acor_order)
acor_est36 <- apply(data36, MARGIN = 1, acor, acor_order = acor_order)
acor_est37 <- apply(data37, MARGIN = 1, acor, acor_order = acor_order)
acor_est38 <- apply(data38, MARGIN = 1, acor, acor_order = acor_order)
acor_est39 <- apply(data39, MARGIN = 1, acor, acor_order = acor_order)
# Function for bootstrap confidence interval
mean_ci_func <- Vectorize(FUN = function(x) {
# TOJ bias-corrected estimation with bootstrap
bootstrap <- boot::boot(data = cbind(mean_est,
mean_est21,
mean_est22,
mean_est23,
mean_est24,
mean_est31,
mean_est32,
mean_est33,
mean_est34,
mean_est35,
mean_est36,
mean_est37,
mean_est38,
mean_est39) - x,
statistic = toj5_boot,
R = R)
estimate <- bootstrap$t0
temp <- bootstrap$t- bootstrap$t0
# Confidence interval
quantile <- apply(temp,
MARGIN = 2,
stats::quantile,
probs = c(0.025, 0.975))
l_ci <- max(0, estimate + quantile[1])
u_ci <- min(1, estimate + quantile[2])
ci <- cbind(l_ci, u_ci)
colnames(ci) <- c("95% CI lower", "95% CI upper")
return(ci)
}, vectorize.args = "x")
acov_ci_func <- Vectorize(FUN = function(x) {
# TOJ bias-corrected estimation with bootstrap
bootstrap <- boot::boot(data = cbind(acov_est,
acov_est21,
acov_est22,
acov_est23,
acov_est24,
acov_est31,
acov_est32,
acov_est33,
acov_est34,
acov_est35,
acov_est36,
acov_est37,
acov_est38,
acov_est39) - x,
statistic = toj5_boot,
R = R)
estimate <- bootstrap$t0
temp <- bootstrap$t- bootstrap$t0
# Confidence interval
quantile <- apply(temp,
MARGIN = 2,
stats::quantile,
probs = c(0.025, 0.975))
l_ci <- max(0, estimate + quantile[1])
u_ci <- min(1, estimate + quantile[2])
ci <- cbind(l_ci, u_ci)
colnames(ci) <- c("95% CI lower", "95% CI upper")
return(ci)
}, vectorize.args = "x")
acor_ci_func <- Vectorize(FUN = function(x) {
# TOJ bias-corrected estimation with bootstrap
bootstrap <- boot::boot(data = cbind(acor_est,
acor_est21,
acor_est22,
acor_est23,
acor_est24,
acor_est31,
acor_est32,
acor_est33,
acor_est34,
acor_est35,
acor_est36,
acor_est37,
acor_est38,
acor_est39) - x,
statistic = toj5_boot,
R = R)
estimate <- bootstrap$t0
temp <- bootstrap$t - bootstrap$t0
# Confidence interval
quantile <- apply(temp,
MARGIN = 2,
stats::quantile,
probs = c(0.025, 0.975))
l_ci <- max(0, estimate + quantile[1])
u_ci <- min(1, estimate + quantile[2])
ci <- cbind(l_ci, u_ci)
colnames(ci) <- c("95% CI lower", "95% CI upper")
return(ci)
}, vectorize.args = "x")
# Limits used for ggplot2
mean_lim <- c(min(mean_est),
max(mean_est))
acov_lim <- c(min(acov_est),
max(acov_est))
acor_lim <- c(min(acor_est),
max(acor_est))
# Compute confidence intervals
if (ci) {
mean_grid <- seq(mean_lim[1], mean_lim[2], length.out = 101)
acov_grid <- seq(acov_lim[1], acov_lim[2], length.out = 101)
acor_grid <- seq(acor_lim[1], acor_lim[2], length.out = 101)
mean_ci <- mean_ci_func(mean_grid)
acov_ci <- acov_ci_func(acov_grid)
acor_ci <- acor_ci_func(acor_grid)
}
# Making figures using ggplot2
if (!ci) {
# Mean
mean_x <- seq(min(mean_est),
max(mean_est),
length = 1000)
mean_y <- tojecdfest5(x = mean_x,
X = mean_est,
X21 = mean_est21,
X22 = mean_est22,
X23 = mean_est23,
X24 = mean_est24,
X31 = mean_est31,
X32 = mean_est32,
X33 = mean_est33,
X34 = mean_est34,
X35 = mean_est35,
X36 = mean_est36,
X37 = mean_est37,
X38 = mean_est38,
X39 = mean_est39)
mean_toj <- Rearrangement::rearrangement(x = data.frame(x = mean_x),
y = mean_y)
mean_plot <- ggplot2::ggplot(data.frame(x = mean_x, y = mean_toj),
ggplot2::aes(x = x, y = y)) +
ggplot2::geom_line() +
ggplot2::xlim(min(mean_est), max(mean_est)) +
ggplot2::ylim(0, 1) +
ggplot2::labs(x = "x", y = "") +
ggplot2::ggtitle("The heterogeneous mean") +
ggplot2::theme_bw()
# Autocovariance
acov_x <- seq(min(acov_est),
max(acov_est),
length = 1000)
acov_y <- tojecdfest5(x = acov_x,
X = acov_est,
X21 = acov_est21,
X22 = acov_est22,
X23 = acov_est23,
X24 = acov_est24,
X31 = acov_est31,
X32 = acov_est32,
X33 = acov_est33,
X34 = acov_est34,
X35 = acov_est35,
X36 = acov_est36,
X37 = acov_est37,
X38 = acov_est38,
X39 = acov_est39)
acov_toj <- Rearrangement::rearrangement(x = data.frame(x = acov_x),
y = acov_y)
acov_plot <- ggplot2::ggplot(data.frame(x = acov_x, y = acov_toj),
ggplot2::aes(x = x, y = y)) +
ggplot2::geom_line() +
ggplot2::xlim(min(acov_est), max(acov_est)) +
ggplot2::ylim(0, 1) +
ggplot2::labs(x = "x", y = "") +
ggplot2::ggtitle("The heterogeneous autocovariance") +
ggplot2::theme_bw()
# Autocorrelation
acor_x <- seq(min(acor_est),
max(acor_est),
length = 1000)
acor_y <- tojecdfest5(x = acor_x,
X = acor_est,
X21 = acor_est21,
X22 = acor_est22,
X23 = acor_est23,
X24 = acor_est24,
X31 = acor_est31,
X32 = acor_est32,
X33 = acor_est33,
X34 = acor_est34,
X35 = acor_est35,
X36 = acor_est36,
X37 = acor_est37,
X38 = acor_est38,
X39 = acor_est39)
acor_toj <- Rearrangement::rearrangement(x = data.frame(x = acor_x),
y = acor_y)
acor_plot <- ggplot2::ggplot(data.frame(x = acor_x, y = acor_toj),
ggplot2::aes(x = x, y = y)) +
ggplot2::geom_line() +
ggplot2::xlim(min(acor_est), max(acor_est)) +
ggplot2::ylim(0, 1) +
ggplot2::labs(x = "x", y = "") +
ggplot2::ggtitle("The heterogeneous autocorrelation") +
ggplot2::theme_bw()
}
if (ci) {
# Mean
mean_toj <- cbind(tojecdfest5(x = mean_grid,
X = mean_est,
X21 = mean_est21,
X22 = mean_est22,
X23 = mean_est23,
X24 = mean_est24,
X31 = mean_est31,
X32 = mean_est32,
X33 = mean_est33,
X34 = mean_est34,
X35 = mean_est35,
X36 = mean_est36,
X37 = mean_est37,
X38 = mean_est38,
X39 = mean_est39),
t(mean_ci))
mean_plot <- ggplot2::ggplot(data = data.frame(x = mean_grid),
ggplot2::aes(x = mean_grid)) +
ggplot2::geom_line(
ggplot2::aes(x = mean_grid,
y = Rearrangement::rearrangement(
x = data.frame(x = mean_grid),
y = mean_toj[, 1])
)
) +
ggplot2::geom_ribbon(
ggplot2::aes(
x = mean_grid,
ymin = Rearrangement::rearrangement(
x = data.frame(x = mean_grid),
y = mean_toj[, 2]),
ymax = Rearrangement::rearrangement(
x = data.frame(x = mean_grid),
y = mean_toj[, 3])
),
alpha = 0.1) +
ggplot2::labs(x = "x", y = "") +
ggplot2::ggtitle("The heterogeneous mean") +
ggplot2::ylim(0, 1) +
ggplot2::theme_bw()
# Autocovariance
acov_toj <- cbind(tojecdfest5(x = acov_grid,
X = acov_est,
X21 = acov_est21,
X22 = acov_est22,
X23 = acov_est23,
X24 = acov_est24,
X31 = acov_est31,
X32 = acov_est32,
X33 = acov_est33,
X34 = acov_est34,
X35 = acov_est35,
X36 = acov_est36,
X37 = acov_est37,
X38 = acov_est38,
X39 = acov_est39),
t(acov_ci))
acov_plot <- ggplot2::ggplot(data = data.frame(x = acov_grid),
ggplot2::aes(x = acov_grid)) +
ggplot2::geom_line(
ggplot2::aes(x = acov_grid,
y = Rearrangement::rearrangement(
x = data.frame(x = acov_grid),
y = acov_toj[, 1])
)
) +
ggplot2::geom_ribbon(
ggplot2::aes(
x = acov_grid,
ymin = Rearrangement::rearrangement(
x = data.frame(x = acov_grid),
y = acov_toj[, 2]),
ymax = Rearrangement::rearrangement(
x = data.frame(x = acov_grid),
y = acov_toj[, 3])
),
alpha = 0.1) +
ggplot2::labs(x = "x", y = "") +
ggplot2::ggtitle("The heterogeneous autocovariance") +
ggplot2::ylim(0, 1) +
ggplot2::theme_bw()
# Autocorrelation
acor_toj <- cbind(tojecdfest5(x = acor_grid,
X = acor_est,
X21 = acor_est21,
X22 = acor_est22,
X23 = acor_est23,
X24 = acor_est24,
X31 = acor_est31,
X32 = acor_est32,
X33 = acor_est33,
X34 = acor_est34,
X35 = acor_est35,
X36 = acor_est36,
X37 = acor_est37,
X38 = acor_est38,
X39 = acor_est39),
t(acor_ci))
acor_plot <- ggplot2::ggplot(data = data.frame(x = acor_grid),
ggplot2::aes(x = acor_grid)) +
ggplot2::geom_line(
ggplot2::aes(x = acor_grid,
y = Rearrangement::rearrangement(
x = data.frame(x = acor_grid),
y = acor_toj[, 1])
)
) +
ggplot2::geom_ribbon(
ggplot2::aes(
x = acor_grid,
ymin = Rearrangement::rearrangement(
x = data.frame(x = acor_grid),
y = acor_toj[, 2]),
ymax = Rearrangement::rearrangement(
x = data.frame(x = acor_grid),
y = acor_toj[, 3])
),
alpha = 0.1) +
ggplot2::labs(x = "x", y = "") +
ggplot2::ggtitle("The heterogeneous autocorrelation") +
ggplot2::ylim(0, 1) +
ggplot2::theme_bw()
}
# Functions without rearrangement
mean_func <- function(x) {
tojecdfest5(x = x,
X = mean_est,
X21 = mean_est21,
X22 = mean_est22,
X23 = mean_est23,
X24 = mean_est24,
X31 = mean_est31,
X32 = mean_est32,
X33 = mean_est33,
X34 = mean_est34,
X35 = mean_est35,
X36 = mean_est36,
X37 = mean_est37,
X38 = mean_est38,
X39 = mean_est39)
}
acov_func <- function(x) {
tojecdfest5(x = x,
X = acov_est,
X21 = acov_est21,
X22 = acov_est22,
X23 = acov_est23,
X24 = acov_est24,
X31 = acov_est31,
X32 = acov_est32,
X33 = acov_est33,
X34 = acov_est34,
X35 = acov_est35,
X36 = acov_est36,
X37 = acov_est37,
X38 = acov_est38,
X39 = acov_est39)
}
acor_func <- function(x) {
tojecdfest5(x = x,
X = acor_est,
X21 = acor_est21,
X22 = acor_est22,
X23 = acor_est23,
X24 = acor_est24,
X31 = acor_est31,
X32 = acor_est32,
X33 = acor_est33,
X34 = acor_est34,
X35 = acor_est35,
X36 = acor_est36,
X37 = acor_est37,
X38 = acor_est38,
X39 = acor_est39)
}
}
# Results
quantity <- cbind(mean_est,
acov_est,
acor_est)
colnames(quantity) <- c("mean",
"autocovariance",
"autocorrelation")
return(list(mean = mean_plot,
acov = acov_plot,
acor = acor_plot,
mean_func = mean_func,
acov_func = acov_func,
acor_func = acor_func,
mean_ci_func = mean_ci_func,
acov_ci_func = acov_ci_func,
acor_ci_func = acor_ci_func,
quantity = quantity,
acov_order = acov_order,
acor_order = acor_order,
N = N,
S = S,
R = R)
)
}
#' Compute TOJ empirical CDF estimate for T equivalent to 0 modulo 6
#'
#' @param x An evaluation point
#' @param X A vector of original cross-sectional data
#' @param X21 A vector of half-panel cross-sectional data 1
#' @param X22 A vector of half-panel cross-sectional data 2
#' @param X31 A vector of third-panel cross-sectional data 1
#' @param X32 A vector of third-panel cross-sectional data 2
#' @param X33 A vector of third-panel cross-sectional data 3
#'
#' @noRd
#'
tojecdfest0 <- Vectorize(FUN = function(x, X, X21, X22, X31, X32, X33) {
# Estimates
est <- mean(X <= x)
est21 <- mean(X21 <= x)
est22 <- mean(X22 <= x)
est31 <- mean(X31 <= x)
est32 <- mean(X32 <= x)
est33 <- mean(X33 <= x)
# TOJ estimate
tojest <- 3.536 * est -
4.072 * (est21 + est22) / 2 +
1.536 * (est31 + est32 + est33) / 3
# Ensure valid estimates
tojest <- ifelse(tojest >= 0, tojest, 0)
tojest <- ifelse(tojest <= 1, tojest, 1)
return(tojest)
}, vectorize.args = "x")
#' Compute TOJ empirical CDF estimate for T equivalent to 1 modulo 6
#'
#' @param x An evaluation point
#' @param X A vector of original cross-sectional data
#' @param X21 A vector of half-panel cross-sectional data 1
#' @param X22 A vector of half-panel cross-sectional data 2
#' @param X23 A vector of half-panel cross-sectional data 3
#' @param X24 A vector of half-panel cross-sectional data 4
#' @param X31 A vector of third-panel cross-sectional data 1
#' @param X32 A vector of third-panel cross-sectional data 2
#' @param X33 A vector of third-panel cross-sectional data 3
#' @param X34 A vector of third-panel cross-sectional data 4
#' @param X35 A vector of third-panel cross-sectional data 5
#' @param X36 A vector of third-panel cross-sectional data 6
#' @param X37 A vector of third-panel cross-sectional data 7
#' @param X38 A vector of third-panel cross-sectional data 8
#' @param X39 A vector of third-panel cross-sectional data 9
#'
#' @noRd
#'
tojecdfest1 <- Vectorize(FUN = function(x,
X,
X21,
X22,
X23,
X24,
X31,
X32,
X33,
X34,
X35,
X36,
X37,
X38,
X39) {
# Estimates
est <- mean(X <= x)
est21 <- mean(X21 <= x)
est22 <- mean(X22 <= x)
est23 <- mean(X23 <= x)
est24 <- mean(X24 <= x)
est31 <- mean(X31 <= x)
est32 <- mean(X32 <= x)
est33 <- mean(X33 <= x)
est34 <- mean(X34 <= x)
est35 <- mean(X35 <= x)
est36 <- mean(X36 <= x)
est37 <- mean(X37 <= x)
est38 <- mean(X38 <= x)
est39 <- mean(X39 <= x)
# TOJ estimate
tojest <- 3.536 * est -
4.072 * (est21 + est22 + est23 + est24) / 4 +
1.536 * (est31 + est32 + est33 + est34 +
est35 + est36 + est37 + est38 + est39) / 9
# Ensure valid estimates
tojest <- ifelse(tojest >= 0, tojest, 0)
tojest <- ifelse(tojest <= 1, tojest, 1)
return(tojest)
}, vectorize.args = "x")
#' Compute TOJ empirical CDF estimate for T equivalent to 2 modulo 6
#'
#' @param x An evaluation point
#' @param X A vector of original cross-sectional data
#' @param X21 A vector of half-panel cross-sectional data 1
#' @param X22 A vector of half-panel cross-sectional data 2
#' @param X31 A vector of third-panel cross-sectional data 1
#' @param X32 A vector of third-panel cross-sectional data 2
#' @param X33 A vector of third-panel cross-sectional data 3
#' @param X34 A vector of third-panel cross-sectional data 4
#' @param X35 A vector of third-panel cross-sectional data 5
#' @param X36 A vector of third-panel cross-sectional data 6
#' @param X37 A vector of third-panel cross-sectional data 7
#' @param X38 A vector of third-panel cross-sectional data 8
#' @param X39 A vector of third-panel cross-sectional data 9
#'
#' @noRd
#'
tojecdfest2 <- Vectorize(FUN = function(x,
X,
X21,
X22,
X31,
X32,
X33,
X34,
X35,
X36,
X37,
X38,
X39) {
# Estimates
est <- mean(X <= x)
est21 <- mean(X21 <= x)
est22 <- mean(X22 <= x)
est31 <- mean(X31 <= x)
est32 <- mean(X32 <= x)
est33 <- mean(X33 <= x)
est34 <- mean(X34 <= x)
est35 <- mean(X35 <= x)
est36 <- mean(X36 <= x)
est37 <- mean(X37 <= x)
est38 <- mean(X38 <= x)
est39 <- mean(X39 <= x)
# TOJ estimate
tojest <- 3.536 * est -
4.072 * (est21 + est22) / 2 +
1.536 * (est31 + est32 + est33 + est34 +
est35 + est36 + est37 + est38 + est39) / 9
# Ensure valid estimates
tojest <- ifelse(tojest >= 0, tojest, 0)
tojest <- ifelse(tojest <= 1, tojest, 1)
return(tojest)
}, vectorize.args = "x")
#' Compute TOJ empirical CDF estimate for T equivalent to 3 modulo 6
#'
#' @param x An evaluation point
#' @param X A vector of original cross-sectional data
#' @param X21 A vector of half-panel cross-sectional data 1
#' @param X22 A vector of half-panel cross-sectional data 2
#' @param X23 A vector of half-panel cross-sectional data 3
#' @param X24 A vector of half-panel cross-sectional data 4
#' @param X31 A vector of third-panel cross-sectional data 1
#' @param X32 A vector of third-panel cross-sectional data 2
#' @param X33 A vector of third-panel cross-sectional data 3
#'
#' @noRd
#'
tojecdfest3 <- Vectorize(FUN = function(x,
X,
X21,
X22,
X23,
X24,
X31,
X32,
X33) {
# Estimates
est <- mean(X <= x)
est21 <- mean(X21 <= x)
est22 <- mean(X22 <= x)
est23 <- mean(X23 <= x)
est24 <- mean(X24 <= x)
est31 <- mean(X31 <= x)
est32 <- mean(X32 <= x)
est33 <- mean(X33 <= x)
# TOJ estimate
tojest <- 3.536 * est -
4.072 * (est21 + est22 + est23 + est24) / 4 +
1.536 * (est31 + est32 + est33) / 3
# Ensure valid estimates
tojest <- ifelse(tojest >= 0, tojest, 0)
tojest <- ifelse(tojest <= 1, tojest, 1)
return(tojest)
}, vectorize.args = "x")
#' Compute TOJ empirical CDF estimate for T equivalent to 4 modulo 6
#'
#' @param x An evaluation point
#' @param X A vector of original cross-sectional data
#' @param X21 A vector of half-panel cross-sectional data 1
#' @param X22 A vector of half-panel cross-sectional data 2
#' @param X31 A vector of third-panel cross-sectional data 1
#' @param X32 A vector of third-panel cross-sectional data 2
#' @param X33 A vector of third-panel cross-sectional data 3
#' @param X34 A vector of third-panel cross-sectional data 4
#' @param X35 A vector of third-panel cross-sectional data 5
#' @param X36 A vector of third-panel cross-sectional data 6
#' @param X37 A vector of third-panel cross-sectional data 7
#' @param X38 A vector of third-panel cross-sectional data 8
#' @param X39 A vector of third-panel cross-sectional data 9
#'
#' @noRd
#'
tojecdfest4 <- Vectorize(FUN = function(x,
X,
X21,
X22,
X31,
X32,
X33,
X34,
X35,
X36,
X37,
X38,
X39) {
# Estimates
est <- mean(X <= x)
est21 <- mean(X21 <= x)
est22 <- mean(X22 <= x)
est31 <- mean(X31 <= x)
est32 <- mean(X32 <= x)
est33 <- mean(X33 <= x)
est34 <- mean(X34 <= x)
est35 <- mean(X35 <= x)
est36 <- mean(X36 <= x)
est37 <- mean(X37 <= x)
est38 <- mean(X38 <= x)
est39 <- mean(X39 <= x)
# TOJ estimate
tojest <- 3.536 * est -
4.072 * (est21 + est22) / 2 +
1.536 * (est31 + est32 + est33 + est34 +
est35 + est36 + est37 + est38 + est39) / 9
# Ensure valid estimates
tojest <- ifelse(tojest >= 0, tojest, 0)
tojest <- ifelse(tojest <= 1, tojest, 1)
return(tojest)
}, vectorize.args = "x")
#' Compute TOJ empirical CDF estimate for T equivalent to 5 modulo 6
#'
#' @param x An evaluation point
#' @param X A vector of original cross-sectional data
#' @param X21 A vector of half-panel cross-sectional data 1
#' @param X22 A vector of half-panel cross-sectional data 2
#' @param X23 A vector of half-panel cross-sectional data 3
#' @param X24 A vector of half-panel cross-sectional data 4
#' @param X31 A vector of third-panel cross-sectional data 1
#' @param X32 A vector of third-panel cross-sectional data 2
#' @param X33 A vector of third-panel cross-sectional data 3
#' @param X34 A vector of third-panel cross-sectional data 4
#' @param X35 A vector of third-panel cross-sectional data 5
#' @param X36 A vector of third-panel cross-sectional data 6
#' @param X37 A vector of third-panel cross-sectional data 7
#' @param X38 A vector of third-panel cross-sectional data 8
#' @param X39 A vector of third-panel cross-sectional data 9
#'
#' @noRd
#'
tojecdfest5 <- Vectorize(FUN = function(x,
X,
X21,
X22,
X23,
X24,
X31,
X32,
X33,
X34,
X35,
X36,
X37,
X38,
X39) {
# Estimates
est <- mean(X <= x)
est21 <- mean(X21 <= x)
est22 <- mean(X22 <= x)
est23 <- mean(X23 <= x)
est24 <- mean(X24 <= x)
est31 <- mean(X31 <= x)
est32 <- mean(X32 <= x)
est33 <- mean(X33 <= x)
est34 <- mean(X34 <= x)
est35 <- mean(X35 <= x)
est36 <- mean(X36 <= x)
est37 <- mean(X37 <= x)
est38 <- mean(X38 <= x)
est39 <- mean(X39 <= x)
# TOJ estimate
tojest <- 3.536 * est -
4.072 * (est21 + est22 + est23 + est24) / 4 +
1.536 * (est31 + est32 + est33 + est34 +
est35 + est36 + est37 + est38 + est39) / 9
# Ensure valid estimates
tojest <- ifelse(tojest >= 0, tojest, 0)
tojest <- ifelse(tojest <= 1, tojest, 1)
return(tojest)
}, vectorize.args = "x")
#' Compute bootstrap TOJ empirical CDF estimate for T equivalent to 0 modulo 6
#'
#' @param quantity An N * 6 matrix of estimates
#' @param indices A vector of indices for bootstrap repetitions
#'
#' @noRd
#'
toj0_boot <- function(quantity, indices) {
# Estimates
est <- mean(quantity[indices, 1] <= 0)
est21 <- mean(quantity[indices, 2] <= 0)
est22 <- mean(quantity[indices, 3] <= 0)
est31 <- mean(quantity[indices, 4] <= 0)
est32 <- mean(quantity[indices, 5] <= 0)
est33 <- mean(quantity[indices, 6] <= 0)
# TOJ estimate
tojest <- 3.536 * est -
4.072 * (est21 + est22) / 2 +
1.536 * (est31 + est32 + est33) / 3
# Ensure valid estimates
tojest <- ifelse(tojest >= 0, tojest, 0)
tojest <- ifelse(tojest <= 1, tojest, 1)
return(tojest)
}
#' Compute bootstrap TOJ empirical CDF estimate for T equivalent to 1 modulo 6
#'
#' @param quantity An N * 14 matrix of estimates
#' @param indices A vector of indices for bootstrap repetitions
#'
#' @noRd
#'
toj1_boot <- function(quantity, indices) {
# Estimates
est <- mean(quantity[indices, 1] <= 0)
est21 <- mean(quantity[indices, 2] <= 0)
est22 <- mean(quantity[indices, 3] <= 0)
est23 <- mean(quantity[indices, 4] <= 0)
est24 <- mean(quantity[indices, 5] <= 0)
est31 <- mean(quantity[indices, 6] <= 0)
est32 <- mean(quantity[indices, 7] <= 0)
est33 <- mean(quantity[indices, 8] <= 0)
est34 <- mean(quantity[indices, 9] <= 0)
est35 <- mean(quantity[indices, 10] <= 0)
est36 <- mean(quantity[indices, 11] <= 0)
est37 <- mean(quantity[indices, 12] <= 0)
est38 <- mean(quantity[indices, 13] <= 0)
est39 <- mean(quantity[indices, 14] <= 0)
# TOJ estimate
tojest <- 3.536 * est -
4.072 * (est21 + est22 + est23 + est24) / 4 +
1.536 * (est31 + est32 + est33 + est34 +
est35 + est36 + est37 + est38 + est39) / 9
# Ensure valid estimates
tojest <- ifelse(tojest >= 0, tojest, 0)
tojest <- ifelse(tojest <= 1, tojest, 1)
return(tojest)
}
#' Compute bootstrap TOJ empirical CDF estimate for T equivalent to 2 modulo 6
#'
#' @param quantity An N * 12 matrix of estimates
#' @param indices A vector of indices for bootstrap repetitions
#'
#' @noRd
#'
toj2_boot <- function(quantity, indices) {
# Estimates
est <- mean(quantity[indices, 1] <= 0)
est21 <- mean(quantity[indices, 2] <= 0)
est22 <- mean(quantity[indices, 3] <= 0)
est31 <- mean(quantity[indices, 4] <= 0)
est32 <- mean(quantity[indices, 5] <= 0)
est33 <- mean(quantity[indices, 6] <= 0)
est34 <- mean(quantity[indices, 7] <= 0)
est35 <- mean(quantity[indices, 8] <= 0)
est36 <- mean(quantity[indices, 9] <= 0)
est37 <- mean(quantity[indices, 10] <= 0)
est38 <- mean(quantity[indices, 11] <= 0)
est39 <- mean(quantity[indices, 12] <= 0)
# TOJ estimate
tojest <- 3.536 * est -
4.072 * (est21 + est22) / 2 +
1.536 * (est31 + est32 + est33 + est34 +
est35 + est36 + est37 + est38 + est39) / 9
# Ensure valid estimates
tojest <- ifelse(tojest >= 0, tojest, 0)
tojest <- ifelse(tojest <= 1, tojest, 1)
return(tojest)
}
#' Compute bootstrap TOJ empirical CDF estimate for T equivalent to 3 modulo 6
#'
#' @param quantity An N * 8 matrix of estimates
#' @param indices A vector of indices for bootstrap repetitions
#'
#' @noRd
#'
toj3_boot <- function(quantity, indices) {
# Estimates
est <- mean(quantity[indices, 1] <= 0)
est21 <- mean(quantity[indices, 2] <= 0)
est22 <- mean(quantity[indices, 3] <= 0)
est23 <- mean(quantity[indices, 4] <= 0)
est24 <- mean(quantity[indices, 5] <= 0)
est31 <- mean(quantity[indices, 6] <= 0)
est32 <- mean(quantity[indices, 7] <= 0)
est33 <- mean(quantity[indices, 8] <= 0)
# TOJ estimate
tojest <- 3.536 * est -
4.072 * (est21 + est22 + est23 + est24) / 4 +
1.536 * (est31 + est32 + est33) / 3
# Ensure valid estimates
tojest <- ifelse(tojest >= 0, tojest, 0)
tojest <- ifelse(tojest <= 1, tojest, 1)
return(tojest)
}
#' Compute bootstrap TOJ empirical CDF estimate for T equivalent to 4 modulo 6
#'
#' @param quantity An N * 12 matrix of estimates
#' @param indices A vector of indices for bootstrap repetitions
#'
#' @noRd
#'
toj4_boot <- function(quantity, indices) {
# Estimates
est <- mean(quantity[indices, 1] <= 0)
est21 <- mean(quantity[indices, 2] <= 0)
est22 <- mean(quantity[indices, 3] <= 0)
est31 <- mean(quantity[indices, 4] <= 0)
est32 <- mean(quantity[indices, 5] <= 0)
est33 <- mean(quantity[indices, 6] <= 0)
est34 <- mean(quantity[indices, 7] <= 0)
est35 <- mean(quantity[indices, 8] <= 0)
est36 <- mean(quantity[indices, 9] <= 0)
est37 <- mean(quantity[indices, 10] <= 0)
est38 <- mean(quantity[indices, 11] <= 0)
est39 <- mean(quantity[indices, 12] <= 0)
# TOJ estimate
tojest <- 3.536 * est -
4.072 * (est21 + est22) / 2 +
1.536 * (est31 + est32 + est33 + est34 +
est35 + est36 + est37 + est38 + est39) / 9
# Ensure valid estimates
tojest <- ifelse(tojest >= 0, tojest, 0)
tojest <- ifelse(tojest <= 1, tojest, 1)
return(tojest)
}
#' Compute bootstrap TOJ empirical CDF estimate for T equivalent to 5 modulo 6
#'
#' @param quantity N * 14 matrix of estimates
#' @param indices A vector of indices for bootstrap repetitions
#'
#' @noRd
#'
toj5_boot <- function(quantity, indices) {
# Estimates
est <- mean(quantity[indices, 1] <= 0)
est21 <- mean(quantity[indices, 2] <= 0)
est22 <- mean(quantity[indices, 3] <= 0)
est23 <- mean(quantity[indices, 4] <= 0)
est24 <- mean(quantity[indices, 5] <= 0)
est31 <- mean(quantity[indices, 6] <= 0)
est32 <- mean(quantity[indices, 7] <= 0)
est33 <- mean(quantity[indices, 8] <= 0)
est34 <- mean(quantity[indices, 9] <= 0)
est35 <- mean(quantity[indices, 10] <= 0)
est36 <- mean(quantity[indices, 11] <= 0)
est37 <- mean(quantity[indices, 12] <= 0)
est38 <- mean(quantity[indices, 13] <= 0)
est39 <- mean(quantity[indices, 14] <= 0)
# TOJ estimate
tojest <- 3.536 * est -
4.072 * (est21 + est22 + est23 + est24) / 4 +
1.536 * (est31 + est32 + est33 + est34 +
est35 + est36 + est37 + est38 + est39) / 9
# Ensure valid estimates
tojest <- ifelse(tojest >= 0, tojest, 0)
tojest <- ifelse(tojest <= 1, tojest, 1)
return(tojest)
}
tkhdyanagi/panelhetero documentation built on June 28, 2023, 1:48 a.m.
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Defines functions toj5_boot toj4_boot toj3_boot toj2_boot toj1_boot toj0_boot tojecdf
Documented in tojecdf
#' The TOJ bias-corrected empirical CDF estimation
#'
#' The `tojecdf()` function enables to implement the TOJ bias-corrected
#' estimation of the cumulative distribution function (CDF) of
#' the heterogeneous mean, the heterogeneous autocovariance, and
#' the heterogeneous autocorrelation.
#' The method is developed by Okui and Yanagi (2019).
#' For more details, see the package vignette with `vignette("panelhetero")`.
#'
#' @param data A matrix of panel data.
#' Each row corresponds to individual time series.
#' @param acov_order A non-negative integer of the order of autocovariance.
#' Default is 0.
#' @param acor_order A positive integer of the order of autocorrelation.
#' Default is 1.
#' @param ci A logical whether to estimate the confidence interval.
#' Default is TRUE.
#' @param R A positive integer of the number of bootstrap repetitions.
#' Default is 1000.
#'
#' @returns A list that contains the following elements.
#' \item{mean}{A plot of the corresponding CDF}
#' \item{acov}{A plot of the corresponding CDF}
#' \item{acor}{A plot of the corresponding CDF}
#' \item{mean_func}{A function that returns the corresponding CDF}
#' \item{acov_func}{A function that returns the corresponding CDF}
#' \item{acor_func}{A function that returns the corresponding CDF}
#' \item{mean_ci_func}{A function that returns the 95 percent confidence
#' interval for the corresponding CDF}
#' \item{acov_ci_func}{A function that returns the 95 percent confidence
#' interval for the corresponding CDF}
#' \item{acor_ci_func}{A function that returns the 95 percent confidence
#' interval for the corresponding CDF}
#' \item{quantity}{A matrix of the estimated heterogeneous quantities}
#' \item{acov_order}{The order of autocovariance}
#' \item{acor_order}{The order of autocorrelation}
#' \item{N}{The number of cross-sectional units}
#' \item{S}{The length of time series}
#' \item{R}{The number of bootstrap repetitions}
#'
#' @examples
#' data <- panelhetero::simulation(N = 300, S = 50)
#' panelhetero::tojecdf(data = data, R = 50)
#'
#' @references Okui, R. and Yanagi, T., 2019.
#' Panel data analysis with heterogeneous dynamics.
#' Journal of Econometrics, 212(2), pp.451-475.
#'
#' @export
#'
tojecdf <- function(data,
acov_order = 0,
acor_order = 1,
R = 1000,
ci = TRUE) {
# Error handling -------------------------------------------------------------
error1(data = data,
acov_order = acov_order,
acor_order = acor_order,
R = R)
# Variable definitions -------------------------------------------------------
x <- y <- NULL
# Omit NA
data <- stats::na.omit(data)
# Sample size
N <- nrow(data)
S <- ncol(data)
# Estimated means, autocovariances, autocorrelations
mean_est <- rowMeans(data)
acov_est <- apply(data, MARGIN = 1, acov, acov_order = acov_order)
acor_est <- apply(data, MARGIN = 1, acor, acor_order = acor_order)
# TOJ bias-corrected estimation ----------------------------------------------
if (S %% 6 == 0) {
# Split panel data for T equivalent to 0 modulo 6
data21 <- data[, 1:(S / 2)]
data22 <- data[, (S / 2 + 1):S]
data31 <- data[, 1:(S / 3)]
data32 <- data[, (S / 3 + 1):(2*S / 3)]
data33 <- data[, (2 * S / 3 + 1):S]
# Estimated quantities for split panel data
mean_est21 <- rowMeans(data21)
mean_est22 <- rowMeans(data22)
mean_est31 <- rowMeans(data31)
mean_est32 <- rowMeans(data32)
mean_est33 <- rowMeans(data33)
acov_est21 <- apply(data21, MARGIN = 1, acov, acov_order = acov_order)
acov_est22 <- apply(data22, MARGIN = 1, acov, acov_order = acov_order)
acov_est31 <- apply(data31, MARGIN = 1, acov, acov_order = acov_order)
acov_est32 <- apply(data32, MARGIN = 1, acov, acov_order = acov_order)
acov_est33 <- apply(data33, MARGIN = 1, acov, acov_order = acov_order)
acor_est21 <- apply(data21, MARGIN = 1, acor, acor_order = acor_order)
acor_est22 <- apply(data22, MARGIN = 1, acor, acor_order = acor_order)
acor_est31 <- apply(data31, MARGIN = 1, acor, acor_order = acor_order)
acor_est32 <- apply(data32, MARGIN = 1, acor, acor_order = acor_order)
acor_est33 <- apply(data33, MARGIN = 1, acor, acor_order = acor_order)
# Function for bootstrap confidence interval
mean_ci_func <- Vectorize(FUN = function(x) {
# TOJ bias-corrected estimation with bootstrap
bootstrap <- boot::boot(data = cbind(mean_est,
mean_est21,
mean_est22,
mean_est31,
mean_est32,
mean_est33) - x,
statistic = toj0_boot,
R = R)
estimate <- bootstrap$t0
temp <- bootstrap$t- bootstrap$t0
# Confidence interval
quantile <- apply(temp,
MARGIN = 2,
stats::quantile,
probs = c(0.025, 0.975))
l_ci <- max(0, estimate + quantile[1])
u_ci <- min(1, estimate + quantile[2])
ci <- cbind(l_ci, u_ci)
colnames(ci) <- c("95% CI lower", "95% CI upper")
return(ci)
}, vectorize.args = "x")
acov_ci_func <- Vectorize(FUN = function(x) {
# TOJ bias-corrected estimation with bootstrap
bootstrap <- boot::boot(data = cbind(acov_est,
acov_est21,
acov_est22,
acov_est31,
acov_est32,
acov_est33) - x,
statistic = toj0_boot,
R = R)
estimate <- bootstrap$t0
temp <- bootstrap$t- bootstrap$t0
# Confidence interval
quantile <- apply(temp,
MARGIN = 2,
stats::quantile,
probs = c(0.025, 0.975))
l_ci <- max(0, estimate + quantile[1])
u_ci <- min(1, estimate + quantile[2])
ci <- cbind(l_ci, u_ci)
colnames(ci) <- c("95% CI lower", "95% CI upper")
return(ci)
}, vectorize.args = "x")
acor_ci_func <- Vectorize(FUN = function(x) {
# TOJ bias-corrected estimation with bootstrap
bootstrap <- boot::boot(data = cbind(acor_est,
acor_est21,
acor_est22,
acor_est31,
acor_est32,
acor_est33) - x,
statistic = toj0_boot,
R = R)
estimate <- bootstrap$t0
temp <- bootstrap$t- bootstrap$t0
# Confidence interval
quantile <- apply(temp,
MARGIN = 2,
stats::quantile,
probs = c(0.025, 0.975))
l_ci <- max(0, estimate + quantile[1])
u_ci <- min(1, estimate + quantile[2])
ci <- cbind(l_ci, u_ci)
colnames(ci) <- c("95% CI lower", "95% CI upper")
return(ci)
}, vectorize.args = "x")
# Limits used for ggplot2
mean_lim <- c(min(mean_est),
max(mean_est))
acov_lim <- c(min(acov_est),
max(acov_est))
acor_lim <- c(min(acor_est),
max(acor_est))
# Compute confidence intervals
if (ci) {
mean_grid <- seq(mean_lim[1], mean_lim[2], length.out = 101)
acov_grid <- seq(acov_lim[1], acov_lim[2], length.out = 101)
acor_grid <- seq(acor_lim[1], acor_lim[2], length.out = 101)
mean_ci <- mean_ci_func(mean_grid)
acov_ci <- acov_ci_func(acov_grid)
acor_ci <- acor_ci_func(acor_grid)
}
# Make figures using ggplot2
if (!ci) {
# Mean
mean_x <- seq(min(mean_est),
max(mean_est),
length = 101)
mean_y <- tojecdfest0(x = mean_x,
X = mean_est,
X21 = mean_est21,
X22 = mean_est22,
X31 = mean_est31,
X32 = mean_est32,
X33 = mean_est33)
mean_toj <- Rearrangement::rearrangement(x = data.frame(x = mean_x),
y = mean_y)
mean_plot <- ggplot2::ggplot(
data.frame(x = mean_x, y = mean_toj),
ggplot2::aes(x = x, y = y)
) +
ggplot2::geom_line() +
ggplot2::xlim(min(mean_est), max(mean_est)) +
ggplot2::ylim(0, 1) +
ggplot2::labs(x = "x", y = "") +
ggplot2::ggtitle("The heterogeneous mean") +
ggplot2::theme_bw()
# Autocovariance
acov_x <- seq(min(acov_est),
max(acov_est),
length = 101)
acov_y <- tojecdfest0(x = acov_x,
X = acov_est,
X21 = acov_est21,
X22 = acov_est22,
X31 = acov_est31,
X32 = acov_est32,
X33 = acov_est33)
acov_toj <- Rearrangement::rearrangement(x = data.frame(x = acov_x),
y = acov_y)
acov_plot <- ggplot2::ggplot(
data.frame(x = acov_x, y = acov_toj),
ggplot2::aes(x = x, y = y)
) +
ggplot2::geom_line() +
ggplot2::xlim(min(acov_est), max(acov_est)) +
ggplot2::ylim(0, 1) +
ggplot2::labs(x = "x", y = "") +
ggplot2::ggtitle("The heterogeneous autocovariance") +
ggplot2::theme_bw()
# Autocorrelation
acor_x <- seq(min(acor_est),
max(acor_est),
length = 101)
acor_y <- tojecdfest0(x = acor_x,
X = acor_est,
X21 = acor_est21,
X22 = acor_est22,
X31 = acor_est31,
X32 = acor_est32,
X33 = acor_est33)
acor_toj <- Rearrangement::rearrangement(x = data.frame(x = acor_x),
y = acor_y)
acor_plot <- ggplot2::ggplot(
data.frame(x = acor_x, y = acor_toj),
ggplot2::aes(x = x, y = y)
) +
ggplot2::geom_line() +
ggplot2::xlim(min(acor_est), max(acor_est)) +
ggplot2::ylim(0, 1) +
ggplot2::labs(x = "x", y = "") +
ggplot2::ggtitle("The heterogeneous autocorrelation") +
ggplot2::theme_bw()
}
if (ci) {
# Mean
mean_toj <- cbind(tojecdfest0(x = mean_grid,
X = mean_est,
X21 = mean_est21,
X22 = mean_est22,
X31 = mean_est31,
X32 = mean_est32,
X33 = mean_est33),
t(mean_ci))
mean_plot <- ggplot2::ggplot(
data = data.frame(x = mean_grid),
ggplot2::aes(x = mean_grid)
) +
ggplot2::geom_line(
ggplot2::aes(
x = mean_grid,
y = Rearrangement::rearrangement(
x = data.frame(x = mean_grid),
y = mean_toj[, 1]
)
)
) +
ggplot2::geom_ribbon(
ggplot2::aes(
x = mean_grid,
ymin = Rearrangement::rearrangement(
x = data.frame(x = mean_grid),
y = mean_toj[, 2]
),
ymax = Rearrangement::rearrangement(
x = data.frame(x = mean_grid),
y = mean_toj[, 3]
)
),
alpha = 0.1) +
ggplot2::labs(x = "x", y = "") +
ggplot2::ggtitle("The heterogeneous mean") +
ggplot2::ylim(0, 1) +
ggplot2::theme_bw()
# Autocovariance
acov_toj <- cbind(tojecdfest0(x = acov_grid,
X = acov_est,
X21 = acov_est21,
X22 = acov_est22,
X31 = acov_est31,
X32 = acov_est32,
X33 = acov_est33),
t(acov_ci))
acov_plot <- ggplot2::ggplot(
data = data.frame(x = acov_grid),
ggplot2::aes(x = acov_grid)
) +
ggplot2::geom_line(
ggplot2::aes(
x = acov_grid,
y = Rearrangement::rearrangement(
x = data.frame(x = acov_grid),
y = acov_toj[, 1]
)
)
) +
ggplot2::geom_ribbon(
ggplot2::aes(
x = acov_grid,
ymin = Rearrangement::rearrangement(
x = data.frame(x = acov_grid),
y = acov_toj[, 2]
),
ymax = Rearrangement::rearrangement(
x = data.frame(x = acov_grid),
y = acov_toj[, 3]
)
),
alpha = 0.1) +
ggplot2::labs(x = "x", y = "") +
ggplot2::ggtitle("The heterogeneous autocovariance") +
ggplot2::ylim(0, 1) +
ggplot2::theme_bw()
# Autocorrelation
acor_toj <- cbind(tojecdfest0(x = acor_grid,
X = acor_est,
X21 = acor_est21,
X22 = acor_est22,
X31 = acor_est31,
X32 = acor_est32,
X33 = acor_est33),
t(acor_ci))
acor_plot <- ggplot2::ggplot(
data = data.frame(x = acor_grid),
ggplot2::aes(x = acor_grid)
) +
ggplot2::geom_line(
ggplot2::aes(
x = acor_grid,
y = Rearrangement::rearrangement(
x = data.frame(x = acor_grid),
y = acor_toj[, 1]
)
)
) +
ggplot2::geom_ribbon(
ggplot2::aes(
x = acor_grid,
ymin = Rearrangement::rearrangement(
x = data.frame(x = acor_grid),
y = acor_toj[, 2]
),
ymax = Rearrangement::rearrangement(
x = data.frame(x = acor_grid),
y = acor_toj[, 3]
)
),
alpha = 0.1) +
ggplot2::labs(x = "x", y = "") +
ggplot2::ggtitle("The heterogeneous autocorrelation") +
ggplot2::ylim(0, 1) +
ggplot2::theme_bw()
}
# Functions without rearrangement
mean_func <- function(x) {
tojecdfest0(x = x,
X = mean_est,
X21 = mean_est21,
X22 = mean_est22,
X31 = mean_est31,
X32 = mean_est32,
X33 = mean_est33)
}
acov_func <- function(x) {
tojecdfest0(x = x,
X = acov_est,
X21 = acov_est21,
X22 = acov_est22,
X31 = acov_est31,
X32 = acov_est32,
X33 = acov_est33)
}
acor_func <- function(x) {
tojecdfest0(x = x,
X = acor_est,
X21 = acor_est21,
X22 = acor_est22,
X31 = acor_est31,
X32 = acor_est32,
X33 = acor_est33)
}
} else if (S %% 6 == 1) {
# Split panel data for T equivalent to 1 modulo 6
data21 <- data[, 1:floor(S / 2)]
data22 <- data[, (floor(S / 2) + 1):S]
data23 <- data[, 1:ceiling(S / 2)]
data24 <- data[, (ceiling(S / 2) + 1):S]
data31 <- data[, 1:floor(S / 3)]
data32 <- data[, (floor(S / 3) + 1):(2 * floor(S / 3))]
data33 <- data[, (2 * floor(S / 3) + 1):S]
data34 <- data[, 1:floor(S / 3)]
data35 <- data[, (floor(S / 3) + 1):(2 * floor(S / 3) + 1)]
data36 <- data[, (2 * floor(S / 3) + 2):S]
data37 <- data[, 1:ceiling(S / 3)]
data38 <- data[, (ceiling(S / 3) + 1):(2 * floor(S / 3) + 1)]
data39 <- data[, (2 * floor(S / 3) + 2):S]
# estimated quantities for split panel data
mean_est21 <- rowMeans(data21)
mean_est22 <- rowMeans(data22)
mean_est23 <- rowMeans(data23)
mean_est24 <- rowMeans(data24)
mean_est31 <- rowMeans(data31)
mean_est32 <- rowMeans(data32)
mean_est33 <- rowMeans(data33)
mean_est34 <- rowMeans(data34)
mean_est35 <- rowMeans(data35)
mean_est36 <- rowMeans(data36)
mean_est37 <- rowMeans(data37)
mean_est38 <- rowMeans(data38)
mean_est39 <- rowMeans(data39)
acov_est21 <- apply(data21, MARGIN = 1, acov, acov_order = acov_order)
acov_est22 <- apply(data22, MARGIN = 1, acov, acov_order = acov_order)
acov_est23 <- apply(data23, MARGIN = 1, acov, acov_order = acov_order)
acov_est24 <- apply(data24, MARGIN = 1, acov, acov_order = acov_order)
acov_est31 <- apply(data31, MARGIN = 1, acov, acov_order = acov_order)
acov_est32 <- apply(data32, MARGIN = 1, acov, acov_order = acov_order)
acov_est33 <- apply(data33, MARGIN = 1, acov, acov_order = acov_order)
acov_est34 <- apply(data34, MARGIN = 1, acov, acov_order = acov_order)
acov_est35 <- apply(data35, MARGIN = 1, acov, acov_order = acov_order)
acov_est36 <- apply(data36, MARGIN = 1, acov, acov_order = acov_order)
acov_est37 <- apply(data37, MARGIN = 1, acov, acov_order = acov_order)
acov_est38 <- apply(data38, MARGIN = 1, acov, acov_order = acov_order)
acov_est39 <- apply(data39, MARGIN = 1, acov, acov_order = acov_order)
acor_est21 <- apply(data21, MARGIN = 1, acor, acor_order = acor_order)
acor_est22 <- apply(data22, MARGIN = 1, acor, acor_order = acor_order)
acor_est23 <- apply(data23, MARGIN = 1, acor, acor_order = acor_order)
acor_est24 <- apply(data24, MARGIN = 1, acor, acor_order = acor_order)
acor_est31 <- apply(data31, MARGIN = 1, acor, acor_order = acor_order)
acor_est32 <- apply(data32, MARGIN = 1, acor, acor_order = acor_order)
acor_est33 <- apply(data33, MARGIN = 1, acor, acor_order = acor_order)
acor_est34 <- apply(data34, MARGIN = 1, acor, acor_order = acor_order)
acor_est35 <- apply(data35, MARGIN = 1, acor, acor_order = acor_order)
acor_est36 <- apply(data36, MARGIN = 1, acor, acor_order = acor_order)
acor_est37 <- apply(data37, MARGIN = 1, acor, acor_order = acor_order)
acor_est38 <- apply(data38, MARGIN = 1, acor, acor_order = acor_order)
acor_est39 <- apply(data39, MARGIN = 1, acor, acor_order = acor_order)
# Function for bootstrap confidence interval
mean_ci_func <- Vectorize(FUN = function(x) {
# TOJ bias-corrected estimation with bootstrap
bootstrap <- boot::boot(data = cbind(mean_est,
mean_est21,
mean_est22,
mean_est23,
mean_est24,
mean_est31,
mean_est32,
mean_est33,
mean_est34,
mean_est35,
mean_est36,
mean_est37,
mean_est38,
mean_est39) - x,
statistic = toj1_boot,
R = R)
estimate <- bootstrap$t0
temp <- bootstrap$t- bootstrap$t0
# Confidence interval
quantile <- apply(temp,
MARGIN = 2,
stats::quantile,
probs = c(0.025, 0.975))
l_ci <- max(0, estimate + quantile[1])
u_ci <- min(1, estimate + quantile[2])
ci <- cbind(l_ci, u_ci)
colnames(ci) <- c("95% CI lower", "95% CI upper")
return(ci)
}, vectorize.args = "x")
acov_ci_func <- Vectorize(FUN = function(x) {
# TOJ bias-corrected estimation with bootstrap
bootstrap <- boot::boot(data = cbind(acov_est,
acov_est21,
acov_est22,
acov_est23,
acov_est24,
acov_est31,
acov_est32,
acov_est33,
acov_est34,
acov_est35,
acov_est36,
acov_est37,
acov_est38,
acov_est39) - x,
statistic = toj1_boot,
R = R)
estimate <- bootstrap$t0
temp <- bootstrap$t- bootstrap$t0
# Confidence interval
quantile <- apply(temp,
MARGIN = 2,
stats::quantile,
probs = c(0.025, 0.975))
l_ci <- max(0, estimate + quantile[1])
u_ci <- min(1, estimate + quantile[2])
ci <- cbind(l_ci, u_ci)
colnames(ci) <- c("95% CI lower", "95% CI upper")
return(ci)
}, vectorize.args = "x")
acor_ci_func <- Vectorize(FUN = function(x) {
# TOJ bias-corrected estimation with bootstrap
bootstrap <- boot::boot(data = cbind(acor_est,
acor_est21,
acor_est22,
acor_est23,
acor_est24,
acor_est31,
acor_est32,
acor_est33,
acor_est34,
acor_est35,
acor_est36,
acor_est37,
acor_est38,
acor_est39) - x,
statistic = toj1_boot,
R = R)
estimate <- bootstrap$t0
temp <- bootstrap$t- bootstrap$t0
# Confidence interval
quantile <- apply(temp,
MARGIN = 2,
stats::quantile,
probs = c(0.025, 0.975))
l_ci <- max(0, estimate + quantile[1])
u_ci <- min(1, estimate + quantile[2])
ci <- cbind(l_ci, u_ci)
colnames(ci) <- c("95% CI lower", "95% CI upper")
return(ci)
}, vectorize.args = "x")
# Limits used for ggplot2
mean_lim <- c(min(mean_est),
max(mean_est))
acov_lim <- c(min(acov_est),
max(acov_est))
acor_lim <- c(min(acor_est),
max(acor_est))
# Compute confidence intervals
if (ci) {
mean_grid <- seq(mean_lim[1], mean_lim[2], length.out = 101)
acov_grid <- seq(acov_lim[1], acov_lim[2], length.out = 101)
acor_grid <- seq(acor_lim[1], acor_lim[2], length.out = 101)
mean_ci <- mean_ci_func(mean_grid)
acov_ci <- acov_ci_func(acov_grid)
acor_ci <- acor_ci_func(acor_grid)
}
# Make figures using ggplot2
if (!ci) {
# Mean
mean_x <- seq(min(mean_est),
max(mean_est),
length = 1000)
mean_y <- tojecdfest1(x = mean_x,
X = mean_est,
X21 = mean_est21,
X22 = mean_est22,
X23 = mean_est23,
X24 = mean_est24,
X31 = mean_est31,
X32 = mean_est32,
X33 = mean_est33,
X34 = mean_est34,
X35 = mean_est35,
X36 = mean_est36,
X37 = mean_est37,
X38 = mean_est38,
X39 = mean_est39)
mean_toj <- Rearrangement::rearrangement(x = data.frame(x = mean_x),
y = mean_y)
mean_plot <- ggplot2::ggplot(data.frame(x = mean_x, y = mean_toj),
ggplot2::aes(x = x, y = y)) +
ggplot2::geom_line() +
ggplot2::xlim(min(mean_est), max(mean_est)) +
ggplot2::ylim(0, 1) +
ggplot2::labs(x = "x", y = "") +
ggplot2::ggtitle("The heterogeneous mean") +
ggplot2::theme_bw()
# Autocovariance
acov_x <- seq(min(acov_est),
max(acov_est),
length = 1000)
acov_y <- tojecdfest1(x = acov_x,
X = acov_est,
X21 = acov_est21,
X22 = acov_est22,
X23 = acov_est23,
X24 = acov_est24,
X31 = acov_est31,
X32 = acov_est32,
X33 = acov_est33,
X34 = acov_est34,
X35 = acov_est35,
X36 = acov_est36,
X37 = acov_est37,
X38 = acov_est38,
X39 = acov_est39)
acov_toj <- Rearrangement::rearrangement(x = data.frame(x = acov_x),
y = acov_y)
acov_plot <- ggplot2::ggplot(data.frame(x = acov_x, y = acov_toj),
ggplot2::aes(x = x, y = y)) +
ggplot2::geom_line() +
ggplot2::xlim(min(acov_est), max(acov_est)) +
ggplot2::ylim(0, 1) +
ggplot2::labs(x = "x", y = "") +
ggplot2::ggtitle("The heterogeneous autocovariance") +
ggplot2::theme_bw()
# Autocorrelation
acor_x <- seq(min(acor_est),
max(acor_est),
length = 1000)
acor_y <- tojecdfest1(x = acor_x,
X = acor_est,
X21 = acor_est21,
X22 = acor_est22,
X23 = acor_est23,
X24 = acor_est24,
X31 = acor_est31,
X32 = acor_est32,
X33 = acor_est33,
X34 = acor_est34,
X35 = acor_est35,
X36 = acor_est36,
X37 = acor_est37,
X38 = acor_est38,
X39 = acor_est39)
acor_toj <- Rearrangement::rearrangement(x = data.frame(x = acor_x),
y = acor_y)
acor_plot <- ggplot2::ggplot(data.frame(x = acor_x, y = acor_toj),
ggplot2::aes(x = x, y = y)) +
ggplot2::geom_line() +
ggplot2::xlim(min(acor_est), max(acor_est)) +
ggplot2::ylim(0, 1) +
ggplot2::labs(x = "x", y = "") +
ggplot2::ggtitle("The heterogeneous autocorrelation") +
ggplot2::theme_bw()
}
if (ci) {
# Mean
mean_toj <- cbind(tojecdfest1(x = mean_grid,
X = mean_est,
X21 = mean_est21,
X22 = mean_est22,
X23 = mean_est23,
X24 = mean_est24,
X31 = mean_est31,
X32 = mean_est32,
X33 = mean_est33,
X34 = mean_est34,
X35 = mean_est35,
X36 = mean_est36,
X37 = mean_est37,
X38 = mean_est38,
X39 = mean_est39),
t(mean_ci))
mean_plot <- ggplot2::ggplot(data = data.frame(x = mean_grid),
ggplot2::aes(x = mean_grid)) +
ggplot2::geom_line(
ggplot2::aes(x = mean_grid,
y = Rearrangement::rearrangement(
x = data.frame(x = mean_grid),
y = mean_toj[, 1])
)
) +
ggplot2::geom_ribbon(
ggplot2::aes(x = mean_grid,
ymin = Rearrangement::rearrangement(
x = data.frame(x = mean_grid),
y = mean_toj[, 2]),
ymax = Rearrangement::rearrangement(
x = data.frame(x = mean_grid),
y = mean_toj[, 3])
), alpha = 0.1) +
ggplot2::labs(x = "x", y = "") +
ggplot2::ggtitle("The heterogeneous mean") +
ggplot2::ylim(0, 1) +
ggplot2::theme_bw()
# Autocovariance
acov_toj <- cbind(tojecdfest1(x = acov_grid,
X = acov_est,
X21 = acov_est21,
X22 = acov_est22,
X23 = acov_est23,
X24 = acov_est24,
X31 = acov_est31,
X32 = acov_est32,
X33 = acov_est33,
X34 = acov_est34,
X35 = acov_est35,
X36 = acov_est36,
X37 = acov_est37,
X38 = acov_est38,
X39 = acov_est39),
t(acov_ci))
acov_plot <- ggplot2::ggplot(data = data.frame(x = acov_grid),
ggplot2::aes(x = acov_grid)) +
ggplot2::geom_line(
ggplot2::aes(x = acov_grid,
y = Rearrangement::rearrangement(
x = data.frame(x = acov_grid),
y = acov_toj[, 1])
)
) +
ggplot2::geom_ribbon(
ggplot2::aes(x = acov_grid,
ymin = Rearrangement::rearrangement(
x = data.frame(x = acov_grid),
y = acov_toj[, 2]),
ymax = Rearrangement::rearrangement(
x = data.frame(x = acov_grid),
y = acov_toj[, 3])
), alpha = 0.1) +
ggplot2::labs(x = "x", y = "") +
ggplot2::ggtitle("The heterogeneous autocovariance") +
ggplot2::ylim(0, 1) +
ggplot2::theme_bw()
# Autocorrelation
acor_toj <- cbind(tojecdfest1(x = acor_grid,
X = acor_est,
X21 = acor_est21,
X22 = acor_est22,
X23 = acor_est23,
X24 = acor_est24,
X31 = acor_est31,
X32 = acor_est32,
X33 = acor_est33,
X34 = acor_est34,
X35 = acor_est35,
X36 = acor_est36,
X37 = acor_est37,
X38 = acor_est38,
X39 = acor_est39),
t(acor_ci))
acor_plot <- ggplot2::ggplot(data = data.frame(x = acor_grid),
ggplot2::aes(x = acor_grid)) +
ggplot2::geom_line(
ggplot2::aes(x = acor_grid,
y = Rearrangement::rearrangement(
x = data.frame(x = acor_grid),
y = acor_toj[, 1])
)
) +
ggplot2::geom_ribbon(
ggplot2::aes(x = acor_grid,
ymin = Rearrangement::rearrangement(
x = data.frame(x = acor_grid),
y = acor_toj[, 2]),
ymax = Rearrangement::rearrangement(
x = data.frame(x = acor_grid),
y = acor_toj[, 3])
), alpha = 0.1) +
ggplot2::labs(x = "x", y = "") +
ggplot2::ggtitle("The heterogeneous autocorrelation") +
ggplot2::ylim(0, 1) +
ggplot2::theme_bw()
}
# Functions without rearrangement
mean_func <- function(x) {
tojecdfest1(x = x,
X = mean_est,
X21 = mean_est21,
X22 = mean_est22,
X23 = mean_est23,
X24 = mean_est24,
X31 = mean_est31,
X32 = mean_est32,
X33 = mean_est33,
X34 = mean_est34,
X35 = mean_est35,
X36 = mean_est36,
X37 = mean_est37,
X38 = mean_est38,
X39 = mean_est39)
}
acov_func <- function(x) {
tojecdfest1(x = x,
X = acov_est,
X21 = acov_est21,
X22 = acov_est22,
X23 = acov_est23,
X24 = acov_est24,
X31 = acov_est31,
X32 = acov_est32,
X33 = acov_est33,
X34 = acov_est34,
X35 = acov_est35,
X36 = acov_est36,
X37 = acov_est37,
X38 = acov_est38,
X39 = acov_est39)
}
acor_func <- function(x) {
tojecdfest1(x = x,
X = acor_est,
X21 = acor_est21,
X22 = acor_est22,
X23 = acor_est23,
X24 = acor_est24,
X31 = acor_est31,
X32 = acor_est32,
X33 = acor_est33,
X34 = acor_est34,
X35 = acor_est35,
X36 = acor_est36,
X37 = acor_est37,
X38 = acor_est38,
X39 = acor_est39)
}
} else if (S %% 6 == 2) {
# Split panel data for T equivalent to 2 modulo 6
data21 <- data[, 1:(S / 2)]
data22 <- data[, (S / 2 + 1):S]
data31 <- data[, 1:floor(S / 3)]
data32 <- data[, (floor(S / 3) + 1):(2 * floor(S / 3) + 1) ]
data33 <- data[, (2 * ceiling(S / 3)):S]
data34 <- data[, 1:ceiling(S / 3)]
data35 <- data[, (ceiling(S / 3) + 1):(2 * floor(S / 3) + 1)]
data36 <- data[, (2 * ceiling(S / 3)):S]
data37 <- data[, 1:ceiling(S / 3)]
data38 <- data[, (ceiling(S / 3) + 1):(2 * ceiling(S / 3))]
data39 <- data[, (2 * ceiling(S / 3) + 1):S]
# Estimated quantities for split panel data
mean_est21 <- rowMeans(data21)
mean_est22 <- rowMeans(data22)
mean_est31 <- rowMeans(data31)
mean_est32 <- rowMeans(data32)
mean_est33 <- rowMeans(data33)
mean_est34 <- rowMeans(data34)
mean_est35 <- rowMeans(data35)
mean_est36 <- rowMeans(data36)
mean_est37 <- rowMeans(data37)
mean_est38 <- rowMeans(data38)
mean_est39 <- rowMeans(data39)
acov_est21 <- apply(data21, MARGIN = 1, acov, acov_order = acov_order)
acov_est22 <- apply(data22, MARGIN = 1, acov, acov_order = acov_order)
acov_est31 <- apply(data31, MARGIN = 1, acov, acov_order = acov_order)
acov_est32 <- apply(data32, MARGIN = 1, acov, acov_order = acov_order)
acov_est33 <- apply(data33, MARGIN = 1, acov, acov_order = acov_order)
acov_est34 <- apply(data34, MARGIN = 1, acov, acov_order = acov_order)
acov_est35 <- apply(data35, MARGIN = 1, acov, acov_order = acov_order)
acov_est36 <- apply(data36, MARGIN = 1, acov, acov_order = acov_order)
acov_est37 <- apply(data37, MARGIN = 1, acov, acov_order = acov_order)
acov_est38 <- apply(data38, MARGIN = 1, acov, acov_order = acov_order)
acov_est39 <- apply(data39, MARGIN = 1, acov, acov_order = acov_order)
acor_est21 <- apply(data21, MARGIN = 1, acor, acor_order = acor_order)
acor_est22 <- apply(data22, MARGIN = 1, acor, acor_order = acor_order)
acor_est31 <- apply(data31, MARGIN = 1, acor, acor_order = acor_order)
acor_est32 <- apply(data32, MARGIN = 1, acor, acor_order = acor_order)
acor_est33 <- apply(data33, MARGIN = 1, acor, acor_order = acor_order)
acor_est34 <- apply(data34, MARGIN = 1, acor, acor_order = acor_order)
acor_est35 <- apply(data35, MARGIN = 1, acor, acor_order = acor_order)
acor_est36 <- apply(data36, MARGIN = 1, acor, acor_order = acor_order)
acor_est37 <- apply(data37, MARGIN = 1, acor, acor_order = acor_order)
acor_est38 <- apply(data38, MARGIN = 1, acor, acor_order = acor_order)
acor_est39 <- apply(data39, MARGIN = 1, acor, acor_order = acor_order)
# Function for bootstrap confidence interval
mean_ci_func <- Vectorize(FUN = function(x) {
# TOJ bias-corrected estimation with bootstrap
bootstrap <- boot::boot(data = cbind(mean_est,
mean_est21,
mean_est22,
mean_est31,
mean_est32,
mean_est33,
mean_est34,
mean_est35,
mean_est36,
mean_est37,
mean_est38,
mean_est39) - x,
statistic = toj2_boot,
R = R)
estimate <- bootstrap$t0
temp <- bootstrap$t- bootstrap$t0
# Confidence interval
quantile <- apply(temp,
MARGIN = 2,
stats::quantile,
probs = c(0.025, 0.975))
l_ci <- max(0, estimate + quantile[1])
u_ci <- min(1, estimate + quantile[2])
ci <- cbind(l_ci, u_ci)
colnames(ci) <- c("95% CI lower", "95% CI upper")
return(ci)
}, vectorize.args = "x")
acov_ci_func <- Vectorize(FUN = function(x) {
# TOJ bias-corrected estimation with bootstrap
bootstrap <- boot::boot(data = cbind(acov_est,
acov_est21,
acov_est22,
acov_est31,
acov_est32,
acov_est33,
acov_est34,
acov_est35,
acov_est36,
acov_est37,
acov_est38,
acov_est39) - x,
statistic = toj2_boot,
R = R)
estimate <- bootstrap$t0
temp <- bootstrap$t- bootstrap$t0
# Confidence interval
quantile <- apply(temp,
MARGIN = 2,
stats::quantile,
probs = c(0.025, 0.975))
l_ci <- max(0, estimate + quantile[1])
u_ci <- min(1, estimate + quantile[2])
ci <- cbind(l_ci, u_ci)
colnames(ci) <- c("95% CI lower", "95% CI upper")
return(ci)
}, vectorize.args = "x")
acor_ci_func <- Vectorize(FUN = function(x) {
# TOJ bias-corrected estimation with bootstrap
bootstrap <- boot::boot(data = cbind(acor_est,
acor_est21,
acor_est22,
acor_est31,
acor_est32,
acor_est33,
acor_est34,
acor_est35,
acor_est36,
acor_est37,
acor_est38,
acor_est39) - x,
statistic = toj2_boot,
R = R)
estimate <- bootstrap$t0
temp <- bootstrap$t- bootstrap$t0
# Confidence interval
quantile <- apply(temp,
MARGIN = 2,
stats::quantile,
probs = c(0.025, 0.975))
l_ci <- max(0, estimate + quantile[1])
u_ci <- min(1, estimate + quantile[2])
ci <- cbind(l_ci, u_ci)
colnames(ci) <- c("95% CI lower", "95% CI upper")
return(ci)
}, vectorize.args = "x")
# Limits used for ggplot2
mean_lim <- c(min(mean_est),
max(mean_est))
acov_lim <- c(min(acov_est),
max(acov_est))
acor_lim <- c(min(acor_est),
max(acor_est))
# Compute confidence intervals
if (ci) {
mean_grid <- seq(mean_lim[1], mean_lim[2], length.out = 101)
acov_grid <- seq(acov_lim[1], acov_lim[2], length.out = 101)
acor_grid <- seq(acor_lim[1], acor_lim[2], length.out = 101)
mean_ci <- mean_ci_func(mean_grid)
acov_ci <- acov_ci_func(acov_grid)
acor_ci <- acor_ci_func(acor_grid)
}
# Make figures using ggplot2
if (!ci) {
# Mean
mean_x <- seq(min(mean_est),
max(mean_est),
length = 1000)
mean_y <- tojecdfest2(x = mean_x,
X = mean_est,
X21 = mean_est21,
X22 = mean_est22,
X31 = mean_est31,
X32 = mean_est32,
X33 = mean_est33,
X34 = mean_est34,
X35 = mean_est35,
X36 = mean_est36,
X37 = mean_est37,
X38 = mean_est38,
X39 = mean_est39)
mean_toj <- Rearrangement::rearrangement(x = data.frame(x = mean_x),
y = mean_y)
mean_plot <- ggplot2::ggplot(data.frame(x = mean_x, y = mean_toj),
ggplot2::aes(x = x, y = y)) +
ggplot2::geom_line() +
ggplot2::xlim(min(mean_est), max(mean_est)) +
ggplot2::ylim(0, 1) +
ggplot2::labs(x = "x", y = "") +
ggplot2::ggtitle("The heterogeneous mean") +
ggplot2::theme_bw()
# Autocovariance
acov_x <- seq(min(acov_est),
max(acov_est),
length = 1000)
acov_y <- tojecdfest2(x = acov_x,
X = acov_est,
X21 = acov_est21,
X22 = acov_est22,
X31 = acov_est31,
X32 = acov_est32,
X33 = acov_est33,
X34 = acov_est34,
X35 = acov_est35,
X36 = acov_est36,
X37 = acov_est37,
X38 = acov_est38,
X39 = acov_est39)
acov_toj <- Rearrangement::rearrangement(x = data.frame(x = acov_x),
y = acov_y)
acov_plot <- ggplot2::ggplot(data.frame(x = acov_x, y = acov_toj),
ggplot2::aes(x = x, y = y)) +
ggplot2::geom_line() +
ggplot2::xlim(min(acov_est), max(acov_est)) +
ggplot2::ylim(0, 1) +
ggplot2::labs(x = "x", y = "") +
ggplot2::ggtitle("The heterogeneous autocovariance") +
ggplot2::theme_bw()
# Autocorrelation
acor_x <- seq(min(acor_est),
max(acor_est),
length = 1000)
acor_y <- tojecdfest2(x = acor_x,
X = acor_est,
X21 = acor_est21,
X22 = acor_est22,
X31 = acor_est31,
X32 = acor_est32,
X33 = acor_est33,
X34 = acor_est34,
X35 = acor_est35,
X36 = acor_est36,
X37 = acor_est37,
X38 = acor_est38,
X39 = acor_est39)
acor_toj <- Rearrangement::rearrangement(x = data.frame(x = acor_x),
y = acor_y)
acor_plot <- ggplot2::ggplot(data.frame(x = acor_x, y = acor_toj),
ggplot2::aes(x = x, y = y)) +
ggplot2::geom_line() +
ggplot2::xlim(min(acor_est), max(acor_est)) +
ggplot2::ylim(0, 1) +
ggplot2::labs(x = "x", y = "") +
ggplot2::ggtitle("The heterogeneous autocorrelation") +
ggplot2::theme_bw()
}
if (ci) {
# Mean
mean_toj <- cbind(tojecdfest2(x = mean_grid,
X = mean_est,
X21 = mean_est21,
X22 = mean_est22,
X31 = mean_est31,
X32 = mean_est32,
X33 = mean_est33,
X34 = mean_est34,
X35 = mean_est35,
X36 = mean_est36,
X37 = mean_est37,
X38 = mean_est38,
X39 = mean_est39),
t(mean_ci))
mean_plot <- ggplot2::ggplot(data = data.frame(x = mean_grid),
ggplot2::aes(x = mean_grid)) +
ggplot2::geom_line(
ggplot2::aes(x = mean_grid,
y = Rearrangement::rearrangement(
x = data.frame(x = mean_grid),
y = mean_toj[, 1])
)
) +
ggplot2::geom_ribbon(
ggplot2::aes(x = mean_grid,
ymin = Rearrangement::rearrangement(
x = data.frame(x = mean_grid),
y = mean_toj[, 2]),
ymax = Rearrangement::rearrangement(
x = data.frame(x = mean_grid),
y = mean_toj[, 3])
),
alpha = 0.1) +
ggplot2::labs(x = "x", y = "") +
ggplot2::ggtitle("The heterogeneous mean") +
ggplot2::ylim(0, 1) +
ggplot2::theme_bw()
# Autocovariance
acov_toj <- cbind(tojecdfest2(x = acov_grid,
X = acov_est,
X21 = acov_est21,
X22 = acov_est22,
X31 = acov_est31,
X32 = acov_est32,
X33 = acov_est33,
X34 = acov_est34,
X35 = acov_est35,
X36 = acov_est36,
X37 = acov_est37,
X38 = acov_est38,
X39 = acov_est39),
t(acov_ci))
acov_plot <- ggplot2::ggplot(data = data.frame(x = acov_grid),
ggplot2::aes(x = acov_grid)) +
ggplot2::geom_line(
ggplot2::aes(x = acov_grid,
y = Rearrangement::rearrangement(
x = data.frame(x = acov_grid),
y = acov_toj[, 1])
)
) +
ggplot2::geom_ribbon(
ggplot2::aes(x = acov_grid,
ymin = Rearrangement::rearrangement(
x = data.frame(x = acov_grid),
y = acov_toj[, 2]),
ymax = Rearrangement::rearrangement(
x = data.frame(x = acov_grid),
y = acov_toj[, 3])
),
alpha = 0.1) +
ggplot2::labs(x = "x", y = "") +
ggplot2::ggtitle("The heterogeneous autocovariance") +
ggplot2::ylim(0, 1) +
ggplot2::theme_bw()
# Autocorrelation
acor_toj <- cbind(tojecdfest2(x = acor_grid,
X = acor_est,
X21 = acor_est21,
X22 = acor_est22,
X31 = acor_est31,
X32 = acor_est32,
X33 = acor_est33,
X34 = acor_est34,
X35 = acor_est35,
X36 = acor_est36,
X37 = acor_est37,
X38 = acor_est38,
X39 = acor_est39),
t(acor_ci))
acor_plot <- ggplot2::ggplot(data = data.frame(x = acor_grid),
ggplot2::aes(x = acor_grid)) +
ggplot2::geom_line(
ggplot2::aes(x = acor_grid,
y = Rearrangement::rearrangement(
x = data.frame(x = acor_grid),
y = acor_toj[, 1])
)
) +
ggplot2::geom_ribbon(
ggplot2::aes(x = acor_grid,
ymin = Rearrangement::rearrangement(
x = data.frame(x = acor_grid),
y = acor_toj[, 2]),
ymax = Rearrangement::rearrangement(
x = data.frame(x = acor_grid),
y = acor_toj[, 3])
),
alpha = 0.1) +
ggplot2::labs(x = "x", y = "") +
ggplot2::ggtitle("The heterogeneous autocorrelation") +
ggplot2::ylim(0, 1) +
ggplot2::theme_bw()
}
# Functions without rearrangement
mean_func <- function(x) {
tojecdfest2(x = x,
X = mean_est,
X21 = mean_est21,
X22 = mean_est22,
X31 = mean_est31,
X32 = mean_est32,
X33 = mean_est33,
X34 = mean_est34,
X35 = mean_est35,
X36 = mean_est36,
X37 = mean_est37,
X38 = mean_est38,
X39 = mean_est39)
}
acov_func <- function(x) {
tojecdfest2(x = x,
X = acov_est,
X21 = acov_est21,
X22 = acov_est22,
X31 = acov_est31,
X32 = acov_est32,
X33 = acov_est33,
X34 = acov_est34,
X35 = acov_est35,
X36 = acov_est36,
X37 = acov_est37,
X38 = acov_est38,
X39 = acov_est39)
}
acor_func <- function(x) {
tojecdfest2(x = x,
X = acor_est,
X21 = acor_est21,
X22 = acor_est22,
X31 = acor_est31,
X32 = acor_est32,
X33 = acor_est33,
X34 = acor_est34,
X35 = acor_est35,
X36 = acor_est36,
X37 = acor_est37,
X38 = acor_est38,
X39 = acor_est39)
}
} else if (S %% 6 == 3) {
# Split panel data for T equivalent to 3 modulo 6
data21 <- data[, 1:floor(S / 2)]
data22 <- data[, (floor(S / 2) + 1):S]
data23 <- data[, 1:ceiling(S / 2)]
data24 <- data[, (ceiling(S / 2) + 1):S]
data31 <- data[, 1:(S / 3)]
data32 <- data[, (S / 3 + 1):(2*S / 3)]
data33 <- data[, (2 * S / 3 + 1):S]
# Estimated quantities for split panel data
mean_est21 <- rowMeans(data21)
mean_est22 <- rowMeans(data22)
mean_est23 <- rowMeans(data23)
mean_est24 <- rowMeans(data24)
mean_est31 <- rowMeans(data31)
mean_est32 <- rowMeans(data32)
mean_est33 <- rowMeans(data33)
acov_est21 <- apply(data21, MARGIN = 1, acov, acov_order = acov_order)
acov_est22 <- apply(data22, MARGIN = 1, acov, acov_order = acov_order)
acov_est23 <- apply(data23, MARGIN = 1, acov, acov_order = acov_order)
acov_est24 <- apply(data24, MARGIN = 1, acov, acov_order = acov_order)
acov_est31 <- apply(data31, MARGIN = 1, acov, acov_order = acov_order)
acov_est32 <- apply(data32, MARGIN = 1, acov, acov_order = acov_order)
acov_est33 <- apply(data33, MARGIN = 1, acov, acov_order = acov_order)
acor_est21 <- apply(data21, MARGIN = 1, acor, acor_order = acor_order)
acor_est22 <- apply(data22, MARGIN = 1, acor, acor_order = acor_order)
acor_est23 <- apply(data23, MARGIN = 1, acor, acor_order = acor_order)
acor_est24 <- apply(data24, MARGIN = 1, acor, acor_order = acor_order)
acor_est31 <- apply(data31, MARGIN = 1, acor, acor_order = acor_order)
acor_est32 <- apply(data32, MARGIN = 1, acor, acor_order = acor_order)
acor_est33 <- apply(data33, MARGIN = 1, acor, acor_order = acor_order)
# Function for bootstrap confidence interval
mean_ci_func <- Vectorize(FUN = function(x) {
# TOJ bias-corrected estimation with bootstrap
bootstrap <- boot::boot(data = cbind(mean_est,
mean_est21,
mean_est22,
mean_est23,
mean_est24,
mean_est31,
mean_est32,
mean_est33) - x,
statistic = toj3_boot,
R = R)
estimate <- bootstrap$t0
temp <- bootstrap$t- bootstrap$t0
# Confidence interval
quantile <- apply(temp,
MARGIN = 2,
stats::quantile,
probs = c(0.025, 0.975))
l_ci <- max(0, estimate + quantile[1])
u_ci <- min(1, estimate + quantile[2])
ci <- cbind(l_ci, u_ci)
colnames(ci) <- c("95% CI lower", "95% CI upper")
return(ci)
}, vectorize.args = "x")
acov_ci_func <- Vectorize(FUN = function(x) {
# TOJ bias-corrected estimation with bootstrap
bootstrap <- boot::boot(data = cbind(acov_est,
acov_est21,
acov_est22,
acov_est23,
acov_est24,
acov_est31,
acov_est32,
acov_est33) - x,
statistic = toj3_boot,
R = R)
estimate <- bootstrap$t0
temp <- bootstrap$t- bootstrap$t0
# Confidence interval
quantile <- apply(temp,
MARGIN = 2,
stats::quantile,
probs = c(0.025, 0.975))
l_ci <- max(0, estimate + quantile[1])
u_ci <- min(1, estimate + quantile[2])
ci <- cbind(l_ci, u_ci)
colnames(ci) <- c("95% CI lower", "95% CI upper")
return(ci)
}, vectorize.args = "x")
acor_ci_func <- Vectorize(FUN = function(x) {
# TOJ bias-corrected estimation with bootstrap
bootstrap <- boot::boot(data = cbind(acor_est,
acor_est21,
acor_est22,
acor_est23,
acor_est24,
acor_est31,
acor_est32,
acor_est33) - x,
statistic = toj3_boot,
R = R)
estimate <- bootstrap$t0
temp <- bootstrap$t- bootstrap$t0
# Confidence interval
quantile <- apply(temp,
MARGIN = 2,
stats::quantile,
probs = c(0.025, 0.975))
l_ci <- max(0, estimate + quantile[1])
u_ci <- min(1, estimate + quantile[2])
ci <- cbind(l_ci, u_ci)
colnames(ci) <- c("95% CI lower", "95% CI upper")
return(ci)
}, vectorize.args = "x")
# Limits used for ggplot2
mean_lim <- c(min(mean_est),
max(mean_est))
acov_lim <- c(min(acov_est),
max(acov_est))
acor_lim <- c(min(acor_est),
max(acor_est))
# Compute confidence intervals
if (ci) {
mean_grid <- seq(mean_lim[1], mean_lim[2], length.out = 101)
acov_grid <- seq(acov_lim[1], acov_lim[2], length.out = 101)
acor_grid <- seq(acor_lim[1], acor_lim[2], length.out = 101)
mean_ci <- mean_ci_func(mean_grid)
acov_ci <- acov_ci_func(acov_grid)
acor_ci <- acor_ci_func(acor_grid)
}
# Make figures using ggplot2
if (!ci) {
# Mean
mean_x <- seq(min(mean_est),
max(mean_est),
length = 1000)
mean_y <- tojecdfest3(x = mean_x,
X = mean_est,
X21 = mean_est21,
X22 = mean_est22,
X23 = mean_est23,
X24 = mean_est24,
X31 = mean_est31,
X32 = mean_est32,
X33 = mean_est33)
mean_toj <- Rearrangement::rearrangement(x = data.frame(x = mean_x),
y = mean_y)
mean_plot <- ggplot2::ggplot(data.frame(x = mean_x, y = mean_toj),
ggplot2::aes(x = x, y = y)) +
ggplot2::geom_line() +
ggplot2::xlim(min(mean_est), max(mean_est)) +
ggplot2::ylim(0, 1) +
ggplot2::labs(x = "x", y = "") +
ggplot2::ggtitle("The heterogeneous mean") +
ggplot2::theme_bw()
# Autocovariance
acov_x <- seq(min(acov_est),
max(acov_est),
length = 1000)
acov_y <- tojecdfest3(x = acov_x,
X = acov_est,
X21 = acov_est21,
X22 = acov_est22,
X23 = acov_est23,
X24 = acov_est24,
X31 = acov_est31,
X32 = acov_est32,
X33 = acov_est33)
acov_toj <- Rearrangement::rearrangement(x = data.frame(x = acov_x),
y = acov_y)
acov_plot <- ggplot2::ggplot(data.frame(x = acov_x, y = acov_toj),
ggplot2::aes(x = x, y = y)) +
ggplot2::geom_line() +
ggplot2::xlim(min(acov_est), max(acov_est)) +
ggplot2::ylim(0, 1) +
ggplot2::labs(x = "x", y = "") +
ggplot2::ggtitle("The heterogeneous autocovariance") +
ggplot2::theme_bw()
# Autocorrelation
acor_x <- seq(min(acor_est),
max(acor_est),
length = 1000)
acor_y <- tojecdfest3(x = acor_x,
X = acor_est,
X21 = acor_est21,
X22 = acor_est22,
X23 = acor_est23,
X24 = acor_est24,
X31 = acor_est31,
X32 = acor_est32,
X33 = acor_est33)
acor_toj <- Rearrangement::rearrangement(x = data.frame(x = acor_x),
y = acor_y)
acor_plot <- ggplot2::ggplot(data.frame(x = acor_x, y = acor_toj),
ggplot2::aes(x = x, y = y)) +
ggplot2::geom_line() +
ggplot2::xlim(min(acor_est), max(acor_est)) +
ggplot2::ylim(0, 1) +
ggplot2::labs(x = "x", y = "") +
ggplot2::ggtitle("The heterogeneous autocorrelation") +
ggplot2::theme_bw()
}
if (ci) {
# Mean
mean_toj <- cbind(tojecdfest3(x = mean_grid,
X = mean_est,
X21 = mean_est21,
X22 = mean_est22,
X23 = mean_est23,
X24 = mean_est24,
X31 = mean_est31,
X32 = mean_est32,
X33 = mean_est33),
t(mean_ci))
mean_plot <- ggplot2::ggplot(data = data.frame(x = mean_grid),
ggplot2::aes(x = mean_grid)) +
ggplot2::geom_line(
ggplot2::aes(x = mean_grid,
y = Rearrangement::rearrangement(
x = data.frame(x = mean_grid),
y = mean_toj[, 1])
)
) +
ggplot2::geom_ribbon(
ggplot2::aes(
x = mean_grid,
ymin = Rearrangement::rearrangement(
x = data.frame(x = mean_grid),
y = mean_toj[, 2]),
ymax = Rearrangement::rearrangement(
x = data.frame(x = mean_grid),
y = mean_toj[, 3])
),
alpha = 0.1) +
ggplot2::labs(x = "x", y = "") +
ggplot2::ggtitle("The heterogeneous mean") +
ggplot2::ylim(0, 1) +
ggplot2::theme_bw()
# Autocovariance
acov_toj <- cbind(tojecdfest3(x = acov_grid,
X = acov_est,
X21 = acov_est21,
X22 = acov_est22,
X23 = acov_est23,
X24 = acov_est24,
X31 = acov_est31,
X32 = acov_est32,
X33 = acov_est33),
t(acov_ci))
acov_plot <- ggplot2::ggplot(data = data.frame(x = acov_grid),
ggplot2::aes(x = acov_grid)) +
ggplot2::geom_line(
ggplot2::aes(x = acov_grid,
y = Rearrangement::rearrangement(
x = data.frame(x = acov_grid),
y = acov_toj[, 1])
)
) +
ggplot2::geom_ribbon(
ggplot2::aes(
x = acov_grid,
ymin = Rearrangement::rearrangement(
x = data.frame(x = acov_grid),
y = acov_toj[, 2]),
ymax = Rearrangement::rearrangement(
x = data.frame(x = acov_grid),
y = acov_toj[, 3])
),
alpha = 0.1) +
ggplot2::labs(x = "x", y = "") +
ggplot2::ggtitle("The heterogeneous autocovariance") +
ggplot2::ylim(0, 1) +
ggplot2::theme_bw()
# Autocorrelation
acor_toj <- cbind(tojecdfest3(x = acor_grid,
X = acor_est,
X21 = acor_est21,
X22 = acor_est22,
X23 = acor_est23,
X24 = acor_est24,
X31 = acor_est31,
X32 = acor_est32,
X33 = acor_est33),
t(acor_ci))
acor_plot <- ggplot2::ggplot(data = data.frame(x = acor_grid),
ggplot2::aes(x = acor_grid)) +
ggplot2::geom_line(
ggplot2::aes(x = acor_grid,
y = Rearrangement::rearrangement(
x = data.frame(x = acor_grid),
y = acor_toj[, 1])
)
) +
ggplot2::geom_ribbon(
ggplot2::aes(
x = acor_grid,
ymin = Rearrangement::rearrangement(
x = data.frame(x = acor_grid),
y = acor_toj[, 2]),
ymax = Rearrangement::rearrangement(
x = data.frame(x = acor_grid),
y = acor_toj[, 3])
),
alpha = 0.1) +
ggplot2::labs(x = "x", y = "") +
ggplot2::ggtitle("The heterogeneous autocorrelation") +
ggplot2::ylim(0, 1) +
ggplot2::theme_bw()
}
# Functions without rearrangement
mean_func <- function(x) {
tojecdfest3(x = x,
X = mean_est,
X21 = mean_est21,
X22 = mean_est22,
X23 = mean_est23,
X24 = mean_est24,
X31 = mean_est31,
X32 = mean_est32,
X33 = mean_est33)
}
acov_func <- function(x) {
tojecdfest3(x = x,
X = acov_est,
X21 = acov_est21,
X22 = acov_est22,
X23 = acov_est23,
X24 = acov_est24,
X31 = acov_est31,
X32 = acov_est32,
X33 = acov_est33)
}
acor_func <- function(x) {
tojecdfest3(x = x,
X = acor_est,
X21 = acor_est21,
X22 = acor_est22,
X23 = acor_est23,
X24 = acor_est24,
X31 = acor_est31,
X32 = acor_est32,
X33 = acor_est33)
}
} else if (S %% 6 == 4) {
# Split panel data for T equivalent to 4 modulo 6
data21 <- data[, 1:(S / 2)]
data22 <- data[, (S / 2 + 1):S]
data31 <- data[, 1:floor(S / 3)]
data32 <- data[, (floor(S / 3) + 1):(2 * floor(S / 3))]
data33 <- data[, (2 * floor(S / 3) + 1):S]
data34 <- data[, 1:floor(S / 3)]
data35 <- data[, (floor(S / 3) + 1):(2 * floor(S / 3) + 1)]
data36 <- data[, (2 * floor(S / 3) + 2):S]
data37 <- data[, 1:ceiling(S / 3)]
data38 <- data[, (ceiling(S / 3) + 1):(2 * floor(S / 3) + 1)]
data39 <- data[, (2 * floor(S / 3) + 2):S]
# Estimated quantities for split panel data
mean_est21 <- rowMeans(data21)
mean_est22 <- rowMeans(data22)
mean_est31 <- rowMeans(data31)
mean_est32 <- rowMeans(data32)
mean_est33 <- rowMeans(data33)
mean_est34 <- rowMeans(data34)
mean_est35 <- rowMeans(data35)
mean_est36 <- rowMeans(data36)
mean_est37 <- rowMeans(data37)
mean_est38 <- rowMeans(data38)
mean_est39 <- rowMeans(data39)
acov_est21 <- apply(data21, MARGIN = 1, acov, acov_order = acov_order)
acov_est22 <- apply(data22, MARGIN = 1, acov, acov_order = acov_order)
acov_est31 <- apply(data31, MARGIN = 1, acov, acov_order = acov_order)
acov_est32 <- apply(data32, MARGIN = 1, acov, acov_order = acov_order)
acov_est33 <- apply(data33, MARGIN = 1, acov, acov_order = acov_order)
acov_est34 <- apply(data34, MARGIN = 1, acov, acov_order = acov_order)
acov_est35 <- apply(data35, MARGIN = 1, acov, acov_order = acov_order)
acov_est36 <- apply(data36, MARGIN = 1, acov, acov_order = acov_order)
acov_est37 <- apply(data37, MARGIN = 1, acov, acov_order = acov_order)
acov_est38 <- apply(data38, MARGIN = 1, acov, acov_order = acov_order)
acov_est39 <- apply(data39, MARGIN = 1, acov, acov_order = acov_order)
acor_est21 <- apply(data21, MARGIN = 1, acor, acor_order = acor_order)
acor_est22 <- apply(data22, MARGIN = 1, acor, acor_order = acor_order)
acor_est31 <- apply(data31, MARGIN = 1, acor, acor_order = acor_order)
acor_est32 <- apply(data32, MARGIN = 1, acor, acor_order = acor_order)
acor_est33 <- apply(data33, MARGIN = 1, acor, acor_order = acor_order)
acor_est34 <- apply(data34, MARGIN = 1, acor, acor_order = acor_order)
acor_est35 <- apply(data35, MARGIN = 1, acor, acor_order = acor_order)
acor_est36 <- apply(data36, MARGIN = 1, acor, acor_order = acor_order)
acor_est37 <- apply(data37, MARGIN = 1, acor, acor_order = acor_order)
acor_est38 <- apply(data38, MARGIN = 1, acor, acor_order = acor_order)
acor_est39 <- apply(data39, MARGIN = 1, acor, acor_order = acor_order)
# Function for bootstrap confidence interval
mean_ci_func <- Vectorize(FUN = function(x) {
# TOJ bias-corrected estimation with bootstrap
bootstrap <- boot::boot(data = cbind(mean_est,
mean_est21,
mean_est22,
mean_est31,
mean_est32,
mean_est33,
mean_est34,
mean_est35,
mean_est36,
mean_est37,
mean_est38,
mean_est39) - x,
statistic = toj4_boot,
R = R)
estimate <- bootstrap$t0
temp <- bootstrap$t- bootstrap$t0
# Confidence interval
quantile <- apply(temp,
MARGIN = 2,
stats::quantile,
probs = c(0.025, 0.975))
l_ci <- max(0, estimate + quantile[1])
u_ci <- min(1, estimate + quantile[2])
ci <- cbind(l_ci, u_ci)
colnames(ci) <- c("95% CI lower", "95% CI upper")
return(ci)
}, vectorize.args = "x")
acov_ci_func <- Vectorize(FUN = function(x) {
# TOJ bias-corrected estimation with bootstrap
bootstrap <- boot::boot(data = cbind(acov_est,
acov_est21,
acov_est22,
acov_est31,
acov_est32,
acov_est33,
acov_est34,
acov_est35,
acov_est36,
acov_est37,
acov_est38,
acov_est39) - x,
statistic = toj4_boot,
R = R)
estimate <- bootstrap$t0
temp <- bootstrap$t- bootstrap$t0
# Confidence interval
quantile <- apply(temp,
MARGIN = 2,
stats::quantile,
probs = c(0.025, 0.975))
l_ci <- max(0, estimate + quantile[1])
u_ci <- min(1, estimate + quantile[2])
ci <- cbind(l_ci, u_ci)
colnames(ci) <- c("95% CI lower", "95% CI upper")
return(ci)
}, vectorize.args = "x")
acor_ci_func <- Vectorize(FUN = function(x) {
# TOJ bias-corrected estimation with bootstrap
bootstrap <- boot::boot(data = cbind(acor_est,
acor_est21,
acor_est22,
acor_est31,
acor_est32,
acor_est33,
acor_est34,
acor_est35,
acor_est36,
acor_est37,
acor_est38,
acor_est39) - x,
statistic = toj4_boot,
R = R)
estimate <- bootstrap$t0
temp <- bootstrap$t- bootstrap$t0
# Confidence interval
quantile <- apply(temp,
MARGIN = 2,
stats::quantile,
probs = c(0.025, 0.975))
l_ci <- max(0, estimate + quantile[1])
u_ci <- min(1, estimate + quantile[2])
ci <- cbind(l_ci, u_ci)
colnames(ci) <- c("95% CI lower", "95% CI upper")
return(ci)
}, vectorize.args = "x")
# Limits used for ggplot2
mean_lim <- c(min(mean_est),
max(mean_est))
acov_lim <- c(min(acov_est),
max(acov_est))
acor_lim <- c(min(acor_est),
max(acor_est))
# Compute confidence intervals
if (ci) {
mean_grid <- seq(mean_lim[1], mean_lim[2], length.out = 101)
acov_grid <- seq(acov_lim[1], acov_lim[2], length.out = 101)
acor_grid <- seq(acor_lim[1], acor_lim[2], length.out = 101)
mean_ci <- mean_ci_func(mean_grid)
acov_ci <- acov_ci_func(acov_grid)
acor_ci <- acor_ci_func(acor_grid)
}
# Make figures using ggplot2
if (!ci) {
# Mean
mean_x <- seq(min(mean_est),
max(mean_est),
length = 1000)
mean_y <- tojecdfest4(x = mean_x,
X = mean_est,
X21 = mean_est21,
X22 = mean_est22,
X31 = mean_est31,
X32 = mean_est32,
X33 = mean_est33,
X34 = mean_est34,
X35 = mean_est35,
X36 = mean_est36,
X37 = mean_est37,
X38 = mean_est38,
X39 = mean_est39)
mean_toj <- Rearrangement::rearrangement(x = data.frame(x = mean_x),
y = mean_y)
mean_plot <- ggplot2::ggplot(data.frame(x = mean_x, y = mean_toj),
ggplot2::aes(x = x, y = y)) +
ggplot2::geom_line() +
ggplot2::xlim(min(mean_est), max(mean_est)) +
ggplot2::ylim(0, 1) +
ggplot2::labs(x = "x", y = "") +
ggplot2::ggtitle("The heterogeneous mean") +
ggplot2::theme_bw()
# Autocovariance
acov_x <- seq(min(acov_est),
max(acov_est),
length = 1000)
acov_y <- tojecdfest4(x = acov_x,
X = acov_est,
X21 = acov_est21,
X22 = acov_est22,
X31 = acov_est31,
X32 = acov_est32,
X33 = acov_est33,
X34 = acov_est34,
X35 = acov_est35,
X36 = acov_est36,
X37 = acov_est37,
X38 = acov_est38,
X39 = acov_est39)
acov_toj <- Rearrangement::rearrangement(x = data.frame(x = acov_x),
y = acov_y)
acov_plot <- ggplot2::ggplot(data.frame(x = acov_x, y = acov_toj),
ggplot2::aes(x = x, y = y)) +
ggplot2::geom_line() +
ggplot2::xlim(min(acov_est), max(acov_est)) +
ggplot2::ylim(0, 1) +
ggplot2::labs(x = "x", y = "") +
ggplot2::ggtitle("The heterogeneous autocovariance") +
ggplot2::theme_bw()
# Autocorrelation
acor_x <- seq(min(acor_est),
max(acor_est),
length = 1000)
acor_y <- tojecdfest4(x = acor_x,
X = acor_est,
X21 = acor_est21,
X22 = acor_est22,
X31 = acor_est31,
X32 = acor_est32,
X33 = acor_est33,
X34 = acor_est34,
X35 = acor_est35,
X36 = acor_est36,
X37 = acor_est37,
X38 = acor_est38,
X39 = acor_est39)
acor_toj <- Rearrangement::rearrangement(x = data.frame(x = acor_x),
y = acor_y)
acor_plot <- ggplot2::ggplot(data.frame(x = acor_x, y = acor_toj),
ggplot2::aes(x = x, y = y)) +
ggplot2::geom_line() +
ggplot2::xlim(min(acor_est), max(acor_est)) +
ggplot2::ylim(0, 1) +
ggplot2::labs(x = "x", y = "") +
ggplot2::ggtitle("The heterogeneous autocorrelation") +
ggplot2::theme_bw()
}
if (ci) {
# Mean
mean_toj <- cbind(tojecdfest4(x = mean_grid,
X = mean_est,
X21 = mean_est21,
X22 = mean_est22,
X31 = mean_est31,
X32 = mean_est32,
X33 = mean_est33,
X34 = mean_est34,
X35 = mean_est35,
X36 = mean_est36,
X37 = mean_est37,
X38 = mean_est38,
X39 = mean_est39),
t(mean_ci))
mean_plot <- ggplot2::ggplot(data = data.frame(x = mean_grid),
ggplot2::aes(x = mean_grid)) +
ggplot2::geom_line(
ggplot2::aes(
x = mean_grid,
y = Rearrangement::rearrangement(
x = data.frame(x = mean_grid),
y = mean_toj[, 1])
)
) +
ggplot2::geom_ribbon(
ggplot2::aes(
x = mean_grid,
ymin = Rearrangement::rearrangement(
x = data.frame(x = mean_grid),
y = mean_toj[, 2]),
ymax = Rearrangement::rearrangement(
x = data.frame(x = mean_grid),
y = mean_toj[, 3])
),
alpha = 0.1) +
ggplot2::labs(x = "x", y = "") +
ggplot2::ggtitle("The heterogeneous mean") +
ggplot2::ylim(0, 1) +
ggplot2::theme_bw()
# Autocovariance
acov_toj <- cbind(tojecdfest4(x = acov_grid,
X = acov_est,
X21 = acov_est21,
X22 = acov_est22,
X31 = acov_est31,
X32 = acov_est32,
X33 = acov_est33,
X34 = acov_est34,
X35 = acov_est35,
X36 = acov_est36,
X37 = acov_est37,
X38 = acov_est38,
X39 = acov_est39),
t(acov_ci))
acov_plot <- ggplot2::ggplot(data = data.frame(x = acov_grid),
ggplot2::aes(x = acov_grid)) +
ggplot2::geom_line(
ggplot2::aes(
x = acov_grid,
y = Rearrangement::rearrangement(
x = data.frame(x = acov_grid),
y = acov_toj[, 1])
)
) +
ggplot2::geom_ribbon(
ggplot2::aes(
x = acov_grid,
ymin = Rearrangement::rearrangement(
x = data.frame(x = acov_grid),
y = acov_toj[, 2]),
ymax = Rearrangement::rearrangement(
x = data.frame(x = acov_grid),
y = acov_toj[, 3])
),
alpha = 0.1) +
ggplot2::labs(x = "x", y = "") +
ggplot2::ggtitle("The heterogeneous autocovariance") +
ggplot2::ylim(0, 1) +
ggplot2::theme_bw()
# Autocorrelation
acor_toj <- cbind(tojecdfest4(x = acor_grid,
X = acor_est,
X21 = acor_est21,
X22 = acor_est22,
X31 = acor_est31,
X32 = acor_est32,
X33 = acor_est33,
X34 = acor_est34,
X35 = acor_est35,
X36 = acor_est36,
X37 = acor_est37,
X38 = acor_est38,
X39 = acor_est39),
t(acor_ci))
acor_plot <- ggplot2::ggplot(data = data.frame(x = acor_grid),
ggplot2::aes(x = acor_grid)) +
ggplot2::geom_line(
ggplot2::aes(
x = acor_grid,
y = Rearrangement::rearrangement(
x = data.frame(x = acor_grid),
y = acor_toj[, 1])
)
) +
ggplot2::geom_ribbon(
ggplot2::aes(
x = acor_grid,
ymin = Rearrangement::rearrangement(
x = data.frame(x = acor_grid),
y = acor_toj[, 2]),
ymax = Rearrangement::rearrangement(
x = data.frame(x = acor_grid),
y = acor_toj[, 3])
),
alpha = 0.1) +
ggplot2::labs(x = "x", y = "") +
ggplot2::ggtitle("The heterogeneous autocorrelation") +
ggplot2::ylim(0, 1) +
ggplot2::theme_bw()
}
# Functions without rearrangement
mean_func <- function(x) {
tojecdfest4(x = x,
X = mean_est,
X21 = mean_est21,
X22 = mean_est22,
X31 = mean_est31,
X32 = mean_est32,
X33 = mean_est33,
X34 = mean_est34,
X35 = mean_est35,
X36 = mean_est36,
X37 = mean_est37,
X38 = mean_est38,
X39 = mean_est39)
}
acov_func <- function(x) {
tojecdfest4(x = x,
X = acov_est,
X21 = acov_est21,
X22 = acov_est22,
X31 = acov_est31,
X32 = acov_est32,
X33 = acov_est33,
X34 = acov_est34,
X35 = acov_est35,
X36 = acov_est36,
X37 = acov_est37,
X38 = acov_est38,
X39 = acov_est39)
}
acor_func <- function(x) {
tojecdfest4(x = x,
X = acor_est,
X21 = acor_est21,
X22 = acor_est22,
X31 = acor_est31,
X32 = acor_est32,
X33 = acor_est33,
X34 = acor_est34,
X35 = acor_est35,
X36 = acor_est36,
X37 = acor_est37,
X38 = acor_est38,
X39 = acor_est39)
}
} else {
# Split panel data for T equivalent to 5 modulo 6
data21 <- data[, 1:floor(S / 2)]
data22 <- data[, (floor(S / 2) + 1):S]
data23 <- data[, 1:ceiling(S / 2)]
data24 <- data[, (ceiling(S / 2) + 1):S]
data31 <- data[, 1:floor(S / 3)]
data32 <- data[, (floor(S / 3) + 1):(2 * floor(S / 3) + 1) ]
data33 <- data[, (2 * ceiling(S / 3)):S]
data34 <- data[, 1:ceiling(S / 3)]
data35 <- data[, (ceiling(S / 3) + 1):(2 * floor(S / 3) + 1)]
data36 <- data[, (2 * ceiling(S / 3)):S]
data37 <- data[, 1:ceiling(S / 3)]
data38 <- data[, (ceiling(S / 3) + 1):(2 * ceiling(S / 3))]
data39 <- data[, (2 * ceiling(S / 3) + 1):S]
# Estimated quantities for split panel data
mean_est21 <- rowMeans(data21)
mean_est22 <- rowMeans(data22)
mean_est23 <- rowMeans(data23)
mean_est24 <- rowMeans(data24)
mean_est31 <- rowMeans(data31)
mean_est32 <- rowMeans(data32)
mean_est33 <- rowMeans(data33)
mean_est34 <- rowMeans(data34)
mean_est35 <- rowMeans(data35)
mean_est36 <- rowMeans(data36)
mean_est37 <- rowMeans(data37)
mean_est38 <- rowMeans(data38)
mean_est39 <- rowMeans(data39)
acov_est21 <- apply(data21, MARGIN = 1, acov, acov_order = acov_order)
acov_est22 <- apply(data22, MARGIN = 1, acov, acov_order = acov_order)
acov_est23 <- apply(data23, MARGIN = 1, acov, acov_order = acov_order)
acov_est24 <- apply(data24, MARGIN = 1, acov, acov_order = acov_order)
acov_est31 <- apply(data31, MARGIN = 1, acov, acov_order = acov_order)
acov_est32 <- apply(data32, MARGIN = 1, acov, acov_order = acov_order)
acov_est33 <- apply(data33, MARGIN = 1, acov, acov_order = acov_order)
acov_est34 <- apply(data34, MARGIN = 1, acov, acov_order = acov_order)
acov_est35 <- apply(data35, MARGIN = 1, acov, acov_order = acov_order)
acov_est36 <- apply(data36, MARGIN = 1, acov, acov_order = acov_order)
acov_est37 <- apply(data37, MARGIN = 1, acov, acov_order = acov_order)
acov_est38 <- apply(data38, MARGIN = 1, acov, acov_order = acov_order)
acov_est39 <- apply(data39, MARGIN = 1, acov, acov_order = acov_order)
acor_est21 <- apply(data21, MARGIN = 1, acor, acor_order = acor_order)
acor_est22 <- apply(data22, MARGIN = 1, acor, acor_order = acor_order)
acor_est23 <- apply(data23, MARGIN = 1, acor, acor_order = acor_order)
acor_est24 <- apply(data24, MARGIN = 1, acor, acor_order = acor_order)
acor_est31 <- apply(data31, MARGIN = 1, acor, acor_order = acor_order)
acor_est32 <- apply(data32, MARGIN = 1, acor, acor_order = acor_order)
acor_est33 <- apply(data33, MARGIN = 1, acor, acor_order = acor_order)
acor_est34 <- apply(data34, MARGIN = 1, acor, acor_order = acor_order)
acor_est35 <- apply(data35, MARGIN = 1, acor, acor_order = acor_order)
acor_est36 <- apply(data36, MARGIN = 1, acor, acor_order = acor_order)
acor_est37 <- apply(data37, MARGIN = 1, acor, acor_order = acor_order)
acor_est38 <- apply(data38, MARGIN = 1, acor, acor_order = acor_order)
acor_est39 <- apply(data39, MARGIN = 1, acor, acor_order = acor_order)
# Function for bootstrap confidence interval
mean_ci_func <- Vectorize(FUN = function(x) {
# TOJ bias-corrected estimation with bootstrap
bootstrap <- boot::boot(data = cbind(mean_est,
mean_est21,
mean_est22,
mean_est23,
mean_est24,
mean_est31,
mean_est32,
mean_est33,
mean_est34,
mean_est35,
mean_est36,
mean_est37,
mean_est38,
mean_est39) - x,
statistic = toj5_boot,
R = R)
estimate <- bootstrap$t0
temp <- bootstrap$t- bootstrap$t0
# Confidence interval
quantile <- apply(temp,
MARGIN = 2,
stats::quantile,
probs = c(0.025, 0.975))
l_ci <- max(0, estimate + quantile[1])
u_ci <- min(1, estimate + quantile[2])
ci <- cbind(l_ci, u_ci)
colnames(ci) <- c("95% CI lower", "95% CI upper")
return(ci)
}, vectorize.args = "x")
acov_ci_func <- Vectorize(FUN = function(x) {
# TOJ bias-corrected estimation with bootstrap
bootstrap <- boot::boot(data = cbind(acov_est,
acov_est21,
acov_est22,
acov_est23,
acov_est24,
acov_est31,
acov_est32,
acov_est33,
acov_est34,
acov_est35,
acov_est36,
acov_est37,
acov_est38,
acov_est39) - x,
statistic = toj5_boot,
R = R)
estimate <- bootstrap$t0
temp <- bootstrap$t- bootstrap$t0
# Confidence interval
quantile <- apply(temp,
MARGIN = 2,
stats::quantile,
probs = c(0.025, 0.975))
l_ci <- max(0, estimate + quantile[1])
u_ci <- min(1, estimate + quantile[2])
ci <- cbind(l_ci, u_ci)
colnames(ci) <- c("95% CI lower", "95% CI upper")
return(ci)
}, vectorize.args = "x")
acor_ci_func <- Vectorize(FUN = function(x) {
# TOJ bias-corrected estimation with bootstrap
bootstrap <- boot::boot(data = cbind(acor_est,
acor_est21,
acor_est22,
acor_est23,
acor_est24,
acor_est31,
acor_est32,
acor_est33,
acor_est34,
acor_est35,
acor_est36,
acor_est37,
acor_est38,
acor_est39) - x,
statistic = toj5_boot,
R = R)
estimate <- bootstrap$t0
temp <- bootstrap$t - bootstrap$t0
# Confidence interval
quantile <- apply(temp,
MARGIN = 2,
stats::quantile,
probs = c(0.025, 0.975))
l_ci <- max(0, estimate + quantile[1])
u_ci <- min(1, estimate + quantile[2])
ci <- cbind(l_ci, u_ci)
colnames(ci) <- c("95% CI lower", "95% CI upper")
return(ci)
}, vectorize.args = "x")
# Limits used for ggplot2
mean_lim <- c(min(mean_est),
max(mean_est))
acov_lim <- c(min(acov_est),
max(acov_est))
acor_lim <- c(min(acor_est),
max(acor_est))
# Compute confidence intervals
if (ci) {
mean_grid <- seq(mean_lim[1], mean_lim[2], length.out = 101)
acov_grid <- seq(acov_lim[1], acov_lim[2], length.out = 101)
acor_grid <- seq(acor_lim[1], acor_lim[2], length.out = 101)
mean_ci <- mean_ci_func(mean_grid)
acov_ci <- acov_ci_func(acov_grid)
acor_ci <- acor_ci_func(acor_grid)
}
# Making figures using ggplot2
if (!ci) {
# Mean
mean_x <- seq(min(mean_est),
max(mean_est),
length = 1000)
mean_y <- tojecdfest5(x = mean_x,
X = mean_est,
X21 = mean_est21,
X22 = mean_est22,
X23 = mean_est23,
X24 = mean_est24,
X31 = mean_est31,
X32 = mean_est32,
X33 = mean_est33,
X34 = mean_est34,
X35 = mean_est35,
X36 = mean_est36,
X37 = mean_est37,
X38 = mean_est38,
X39 = mean_est39)
mean_toj <- Rearrangement::rearrangement(x = data.frame(x = mean_x),
y = mean_y)
mean_plot <- ggplot2::ggplot(data.frame(x = mean_x, y = mean_toj),
ggplot2::aes(x = x, y = y)) +
ggplot2::geom_line() +
ggplot2::xlim(min(mean_est), max(mean_est)) +
ggplot2::ylim(0, 1) +
ggplot2::labs(x = "x", y = "") +
ggplot2::ggtitle("The heterogeneous mean") +
ggplot2::theme_bw()
# Autocovariance
acov_x <- seq(min(acov_est),
max(acov_est),
length = 1000)
acov_y <- tojecdfest5(x = acov_x,
X = acov_est,
X21 = acov_est21,
X22 = acov_est22,
X23 = acov_est23,
X24 = acov_est24,
X31 = acov_est31,
X32 = acov_est32,
X33 = acov_est33,
X34 = acov_est34,
X35 = acov_est35,
X36 = acov_est36,
X37 = acov_est37,
X38 = acov_est38,
X39 = acov_est39)
acov_toj <- Rearrangement::rearrangement(x = data.frame(x = acov_x),
y = acov_y)
acov_plot <- ggplot2::ggplot(data.frame(x = acov_x, y = acov_toj),
ggplot2::aes(x = x, y = y)) +
ggplot2::geom_line() +
ggplot2::xlim(min(acov_est), max(acov_est)) +
ggplot2::ylim(0, 1) +
ggplot2::labs(x = "x", y = "") +
ggplot2::ggtitle("The heterogeneous autocovariance") +
ggplot2::theme_bw()
# Autocorrelation
acor_x <- seq(min(acor_est),
max(acor_est),
length = 1000)
acor_y <- tojecdfest5(x = acor_x,
X = acor_est,
X21 = acor_est21,
X22 = acor_est22,
X23 = acor_est23,
X24 = acor_est24,
X31 = acor_est31,
X32 = acor_est32,
X33 = acor_est33,
X34 = acor_est34,
X35 = acor_est35,
X36 = acor_est36,
X37 = acor_est37,
X38 = acor_est38,
X39 = acor_est39)
acor_toj <- Rearrangement::rearrangement(x = data.frame(x = acor_x),
y = acor_y)
acor_plot <- ggplot2::ggplot(data.frame(x = acor_x, y = acor_toj),
ggplot2::aes(x = x, y = y)) +
ggplot2::geom_line() +
ggplot2::xlim(min(acor_est), max(acor_est)) +
ggplot2::ylim(0, 1) +
ggplot2::labs(x = "x", y = "") +
ggplot2::ggtitle("The heterogeneous autocorrelation") +
ggplot2::theme_bw()
}
if (ci) {
# Mean
mean_toj <- cbind(tojecdfest5(x = mean_grid,
X = mean_est,
X21 = mean_est21,
X22 = mean_est22,
X23 = mean_est23,
X24 = mean_est24,
X31 = mean_est31,
X32 = mean_est32,
X33 = mean_est33,
X34 = mean_est34,
X35 = mean_est35,
X36 = mean_est36,
X37 = mean_est37,
X38 = mean_est38,
X39 = mean_est39),
t(mean_ci))
mean_plot <- ggplot2::ggplot(data = data.frame(x = mean_grid),
ggplot2::aes(x = mean_grid)) +
ggplot2::geom_line(
ggplot2::aes(x = mean_grid,
y = Rearrangement::rearrangement(
x = data.frame(x = mean_grid),
y = mean_toj[, 1])
)
) +
ggplot2::geom_ribbon(
ggplot2::aes(
x = mean_grid,
ymin = Rearrangement::rearrangement(
x = data.frame(x = mean_grid),
y = mean_toj[, 2]),
ymax = Rearrangement::rearrangement(
x = data.frame(x = mean_grid),
y = mean_toj[, 3])
),
alpha = 0.1) +
ggplot2::labs(x = "x", y = "") +
ggplot2::ggtitle("The heterogeneous mean") +
ggplot2::ylim(0, 1) +
ggplot2::theme_bw()
# Autocovariance
acov_toj <- cbind(tojecdfest5(x = acov_grid,
X = acov_est,
X21 = acov_est21,
X22 = acov_est22,
X23 = acov_est23,
X24 = acov_est24,
X31 = acov_est31,
X32 = acov_est32,
X33 = acov_est33,
X34 = acov_est34,
X35 = acov_est35,
X36 = acov_est36,
X37 = acov_est37,
X38 = acov_est38,
X39 = acov_est39),
t(acov_ci))
acov_plot <- ggplot2::ggplot(data = data.frame(x = acov_grid),
ggplot2::aes(x = acov_grid)) +
ggplot2::geom_line(
ggplot2::aes(x = acov_grid,
y = Rearrangement::rearrangement(
x = data.frame(x = acov_grid),
y = acov_toj[, 1])
)
) +
ggplot2::geom_ribbon(
ggplot2::aes(
x = acov_grid,
ymin = Rearrangement::rearrangement(
x = data.frame(x = acov_grid),
y = acov_toj[, 2]),
ymax = Rearrangement::rearrangement(
x = data.frame(x = acov_grid),
y = acov_toj[, 3])
),
alpha = 0.1) +
ggplot2::labs(x = "x", y = "") +
ggplot2::ggtitle("The heterogeneous autocovariance") +
ggplot2::ylim(0, 1) +
ggplot2::theme_bw()
# Autocorrelation
acor_toj <- cbind(tojecdfest5(x = acor_grid,
X = acor_est,
X21 = acor_est21,
X22 = acor_est22,
X23 = acor_est23,
X24 = acor_est24,
X31 = acor_est31,
X32 = acor_est32,
X33 = acor_est33,
X34 = acor_est34,
X35 = acor_est35,
X36 = acor_est36,
X37 = acor_est37,
X38 = acor_est38,
X39 = acor_est39),
t(acor_ci))
acor_plot <- ggplot2::ggplot(data = data.frame(x = acor_grid),
ggplot2::aes(x = acor_grid)) +
ggplot2::geom_line(
ggplot2::aes(x = acor_grid,
y = Rearrangement::rearrangement(
x = data.frame(x = acor_grid),
y = acor_toj[, 1])
)
) +
ggplot2::geom_ribbon(
ggplot2::aes(
x = acor_grid,
ymin = Rearrangement::rearrangement(
x = data.frame(x = acor_grid),
y = acor_toj[, 2]),
ymax = Rearrangement::rearrangement(
x = data.frame(x = acor_grid),
y = acor_toj[, 3])
),
alpha = 0.1) +
ggplot2::labs(x = "x", y = "") +
ggplot2::ggtitle("The heterogeneous autocorrelation") +
ggplot2::ylim(0, 1) +
ggplot2::theme_bw()
}
# Functions without rearrangement
mean_func <- function(x) {
tojecdfest5(x = x,
X = mean_est,
X21 = mean_est21,
X22 = mean_est22,
X23 = mean_est23,
X24 = mean_est24,
X31 = mean_est31,
X32 = mean_est32,
X33 = mean_est33,
X34 = mean_est34,
X35 = mean_est35,
X36 = mean_est36,
X37 = mean_est37,
X38 = mean_est38,
X39 = mean_est39)
}
acov_func <- function(x) {
tojecdfest5(x = x,
X = acov_est,
X21 = acov_est21,
X22 = acov_est22,
X23 = acov_est23,
X24 = acov_est24,
X31 = acov_est31,
X32 = acov_est32,
X33 = acov_est33,
X34 = acov_est34,
X35 = acov_est35,
X36 = acov_est36,
X37 = acov_est37,
X38 = acov_est38,
X39 = acov_est39)
}
acor_func <- function(x) {
tojecdfest5(x = x,
X = acor_est,
X21 = acor_est21,
X22 = acor_est22,
X23 = acor_est23,
X24 = acor_est24,
X31 = acor_est31,
X32 = acor_est32,
X33 = acor_est33,
X34 = acor_est34,
X35 = acor_est35,
X36 = acor_est36,
X37 = acor_est37,
X38 = acor_est38,
X39 = acor_est39)
}
}
# Results
quantity <- cbind(mean_est,
acov_est,
acor_est)
colnames(quantity) <- c("mean",
"autocovariance",
"autocorrelation")
return(list(mean = mean_plot,
acov = acov_plot,
acor = acor_plot,
mean_func = mean_func,
acov_func = acov_func,
acor_func = acor_func,
mean_ci_func = mean_ci_func,
acov_ci_func = acov_ci_func,
acor_ci_func = acor_ci_func,
quantity = quantity,
acov_order = acov_order,
acor_order = acor_order,
N = N,
S = S,
R = R)
)
}
#' Compute TOJ empirical CDF estimate for T equivalent to 0 modulo 6
#'
#' @param x An evaluation point
#' @param X A vector of original cross-sectional data
#' @param X21 A vector of half-panel cross-sectional data 1
#' @param X22 A vector of half-panel cross-sectional data 2
#' @param X31 A vector of third-panel cross-sectional data 1
#' @param X32 A vector of third-panel cross-sectional data 2
#' @param X33 A vector of third-panel cross-sectional data 3
#'
#' @noRd
#'
tojecdfest0 <- Vectorize(FUN = function(x, X, X21, X22, X31, X32, X33) {
# Estimates
est <- mean(X <= x)
est21 <- mean(X21 <= x)
est22 <- mean(X22 <= x)
est31 <- mean(X31 <= x)
est32 <- mean(X32 <= x)
est33 <- mean(X33 <= x)
# TOJ estimate
tojest <- 3.536 * est -
4.072 * (est21 + est22) / 2 +
1.536 * (est31 + est32 + est33) / 3
# Ensure valid estimates
tojest <- ifelse(tojest >= 0, tojest, 0)
tojest <- ifelse(tojest <= 1, tojest, 1)
return(tojest)
}, vectorize.args = "x")
#' Compute TOJ empirical CDF estimate for T equivalent to 1 modulo 6
#'
#' @param x An evaluation point
#' @param X A vector of original cross-sectional data
#' @param X21 A vector of half-panel cross-sectional data 1
#' @param X22 A vector of half-panel cross-sectional data 2
#' @param X23 A vector of half-panel cross-sectional data 3
#' @param X24 A vector of half-panel cross-sectional data 4
#' @param X31 A vector of third-panel cross-sectional data 1
#' @param X32 A vector of third-panel cross-sectional data 2
#' @param X33 A vector of third-panel cross-sectional data 3
#' @param X34 A vector of third-panel cross-sectional data 4
#' @param X35 A vector of third-panel cross-sectional data 5
#' @param X36 A vector of third-panel cross-sectional data 6
#' @param X37 A vector of third-panel cross-sectional data 7
#' @param X38 A vector of third-panel cross-sectional data 8
#' @param X39 A vector of third-panel cross-sectional data 9
#'
#' @noRd
#'
tojecdfest1 <- Vectorize(FUN = function(x,
X,
X21,
X22,
X23,
X24,
X31,
X32,
X33,
X34,
X35,
X36,
X37,
X38,
X39) {
# Estimates
est <- mean(X <= x)
est21 <- mean(X21 <= x)
est22 <- mean(X22 <= x)
est23 <- mean(X23 <= x)
est24 <- mean(X24 <= x)
est31 <- mean(X31 <= x)
est32 <- mean(X32 <= x)
est33 <- mean(X33 <= x)
est34 <- mean(X34 <= x)
est35 <- mean(X35 <= x)
est36 <- mean(X36 <= x)
est37 <- mean(X37 <= x)
est38 <- mean(X38 <= x)
est39 <- mean(X39 <= x)
# TOJ estimate
tojest <- 3.536 * est -
4.072 * (est21 + est22 + est23 + est24) / 4 +
1.536 * (est31 + est32 + est33 + est34 +
est35 + est36 + est37 + est38 + est39) / 9
# Ensure valid estimates
tojest <- ifelse(tojest >= 0, tojest, 0)
tojest <- ifelse(tojest <= 1, tojest, 1)
return(tojest)
}, vectorize.args = "x")
#' Compute TOJ empirical CDF estimate for T equivalent to 2 modulo 6
#'
#' @param x An evaluation point
#' @param X A vector of original cross-sectional data
#' @param X21 A vector of half-panel cross-sectional data 1
#' @param X22 A vector of half-panel cross-sectional data 2
#' @param X31 A vector of third-panel cross-sectional data 1
#' @param X32 A vector of third-panel cross-sectional data 2
#' @param X33 A vector of third-panel cross-sectional data 3
#' @param X34 A vector of third-panel cross-sectional data 4
#' @param X35 A vector of third-panel cross-sectional data 5
#' @param X36 A vector of third-panel cross-sectional data 6
#' @param X37 A vector of third-panel cross-sectional data 7
#' @param X38 A vector of third-panel cross-sectional data 8
#' @param X39 A vector of third-panel cross-sectional data 9
#'
#' @noRd
#'
tojecdfest2 <- Vectorize(FUN = function(x,
X,
X21,
X22,
X31,
X32,
X33,
X34,
X35,
X36,
X37,
X38,
X39) {
# Estimates
est <- mean(X <= x)
est21 <- mean(X21 <= x)
est22 <- mean(X22 <= x)
est31 <- mean(X31 <= x)
est32 <- mean(X32 <= x)
est33 <- mean(X33 <= x)
est34 <- mean(X34 <= x)
est35 <- mean(X35 <= x)
est36 <- mean(X36 <= x)
est37 <- mean(X37 <= x)
est38 <- mean(X38 <= x)
est39 <- mean(X39 <= x)
# TOJ estimate
tojest <- 3.536 * est -
4.072 * (est21 + est22) / 2 +
1.536 * (est31 + est32 + est33 + est34 +
est35 + est36 + est37 + est38 + est39) / 9
# Ensure valid estimates
tojest <- ifelse(tojest >= 0, tojest, 0)
tojest <- ifelse(tojest <= 1, tojest, 1)
return(tojest)
}, vectorize.args = "x")
#' Compute TOJ empirical CDF estimate for T equivalent to 3 modulo 6
#'
#' @param x An evaluation point
#' @param X A vector of original cross-sectional data
#' @param X21 A vector of half-panel cross-sectional data 1
#' @param X22 A vector of half-panel cross-sectional data 2
#' @param X23 A vector of half-panel cross-sectional data 3
#' @param X24 A vector of half-panel cross-sectional data 4
#' @param X31 A vector of third-panel cross-sectional data 1
#' @param X32 A vector of third-panel cross-sectional data 2
#' @param X33 A vector of third-panel cross-sectional data 3
#'
#' @noRd
#'
tojecdfest3 <- Vectorize(FUN = function(x,
X,
X21,
X22,
X23,
X24,
X31,
X32,
X33) {
# Estimates
est <- mean(X <= x)
est21 <- mean(X21 <= x)
est22 <- mean(X22 <= x)
est23 <- mean(X23 <= x)
est24 <- mean(X24 <= x)
est31 <- mean(X31 <= x)
est32 <- mean(X32 <= x)
est33 <- mean(X33 <= x)
# TOJ estimate
tojest <- 3.536 * est -
4.072 * (est21 + est22 + est23 + est24) / 4 +
1.536 * (est31 + est32 + est33) / 3
# Ensure valid estimates
tojest <- ifelse(tojest >= 0, tojest, 0)
tojest <- ifelse(tojest <= 1, tojest, 1)
return(tojest)
}, vectorize.args = "x")
#' Compute TOJ empirical CDF estimate for T equivalent to 4 modulo 6
#'
#' @param x An evaluation point
#' @param X A vector of original cross-sectional data
#' @param X21 A vector of half-panel cross-sectional data 1
#' @param X22 A vector of half-panel cross-sectional data 2
#' @param X31 A vector of third-panel cross-sectional data 1
#' @param X32 A vector of third-panel cross-sectional data 2
#' @param X33 A vector of third-panel cross-sectional data 3
#' @param X34 A vector of third-panel cross-sectional data 4
#' @param X35 A vector of third-panel cross-sectional data 5
#' @param X36 A vector of third-panel cross-sectional data 6
#' @param X37 A vector of third-panel cross-sectional data 7
#' @param X38 A vector of third-panel cross-sectional data 8
#' @param X39 A vector of third-panel cross-sectional data 9
#'
#' @noRd
#'
tojecdfest4 <- Vectorize(FUN = function(x,
X,
X21,
X22,
X31,
X32,
X33,
X34,
X35,
X36,
X37,
X38,
X39) {
# Estimates
est <- mean(X <= x)
est21 <- mean(X21 <= x)
est22 <- mean(X22 <= x)
est31 <- mean(X31 <= x)
est32 <- mean(X32 <= x)
est33 <- mean(X33 <= x)
est34 <- mean(X34 <= x)
est35 <- mean(X35 <= x)
est36 <- mean(X36 <= x)
est37 <- mean(X37 <= x)
est38 <- mean(X38 <= x)
est39 <- mean(X39 <= x)
# TOJ estimate
tojest <- 3.536 * est -
4.072 * (est21 + est22) / 2 +
1.536 * (est31 + est32 + est33 + est34 +
est35 + est36 + est37 + est38 + est39) / 9
# Ensure valid estimates
tojest <- ifelse(tojest >= 0, tojest, 0)
tojest <- ifelse(tojest <= 1, tojest, 1)
return(tojest)
}, vectorize.args = "x")
#' Compute TOJ empirical CDF estimate for T equivalent to 5 modulo 6
#'
#' @param x An evaluation point
#' @param X A vector of original cross-sectional data
#' @param X21 A vector of half-panel cross-sectional data 1
#' @param X22 A vector of half-panel cross-sectional data 2
#' @param X23 A vector of half-panel cross-sectional data 3
#' @param X24 A vector of half-panel cross-sectional data 4
#' @param X31 A vector of third-panel cross-sectional data 1
#' @param X32 A vector of third-panel cross-sectional data 2
#' @param X33 A vector of third-panel cross-sectional data 3
#' @param X34 A vector of third-panel cross-sectional data 4
#' @param X35 A vector of third-panel cross-sectional data 5
#' @param X36 A vector of third-panel cross-sectional data 6
#' @param X37 A vector of third-panel cross-sectional data 7
#' @param X38 A vector of third-panel cross-sectional data 8
#' @param X39 A vector of third-panel cross-sectional data 9
#'
#' @noRd
#'
tojecdfest5 <- Vectorize(FUN = function(x,
X,
X21,
X22,
X23,
X24,
X31,
X32,
X33,
X34,
X35,
X36,
X37,
X38,
X39) {
# Estimates
est <- mean(X <= x)
est21 <- mean(X21 <= x)
est22 <- mean(X22 <= x)
est23 <- mean(X23 <= x)
est24 <- mean(X24 <= x)
est31 <- mean(X31 <= x)
est32 <- mean(X32 <= x)
est33 <- mean(X33 <= x)
est34 <- mean(X34 <= x)
est35 <- mean(X35 <= x)
est36 <- mean(X36 <= x)
est37 <- mean(X37 <= x)
est38 <- mean(X38 <= x)
est39 <- mean(X39 <= x)
# TOJ estimate
tojest <- 3.536 * est -
4.072 * (est21 + est22 + est23 + est24) / 4 +
1.536 * (est31 + est32 + est33 + est34 +
est35 + est36 + est37 + est38 + est39) / 9
# Ensure valid estimates
tojest <- ifelse(tojest >= 0, tojest, 0)
tojest <- ifelse(tojest <= 1, tojest, 1)
return(tojest)
}, vectorize.args = "x")
#' Compute bootstrap TOJ empirical CDF estimate for T equivalent to 0 modulo 6
#'
#' @param quantity An N * 6 matrix of estimates
#' @param indices A vector of indices for bootstrap repetitions
#'
#' @noRd
#'
toj0_boot <- function(quantity, indices) {
# Estimates
est <- mean(quantity[indices, 1] <= 0)
est21 <- mean(quantity[indices, 2] <= 0)
est22 <- mean(quantity[indices, 3] <= 0)
est31 <- mean(quantity[indices, 4] <= 0)
est32 <- mean(quantity[indices, 5] <= 0)
est33 <- mean(quantity[indices, 6] <= 0)
# TOJ estimate
tojest <- 3.536 * est -
4.072 * (est21 + est22) / 2 +
1.536 * (est31 + est32 + est33) / 3
# Ensure valid estimates
tojest <- ifelse(tojest >= 0, tojest, 0)
tojest <- ifelse(tojest <= 1, tojest, 1)
return(tojest)
}
#' Compute bootstrap TOJ empirical CDF estimate for T equivalent to 1 modulo 6
#'
#' @param quantity An N * 14 matrix of estimates
#' @param indices A vector of indices for bootstrap repetitions
#'
#' @noRd
#'
toj1_boot <- function(quantity, indices) {
# Estimates
est <- mean(quantity[indices, 1] <= 0)
est21 <- mean(quantity[indices, 2] <= 0)
est22 <- mean(quantity[indices, 3] <= 0)
est23 <- mean(quantity[indices, 4] <= 0)
est24 <- mean(quantity[indices, 5] <= 0)
est31 <- mean(quantity[indices, 6] <= 0)
est32 <- mean(quantity[indices, 7] <= 0)
est33 <- mean(quantity[indices, 8] <= 0)
est34 <- mean(quantity[indices, 9] <= 0)
est35 <- mean(quantity[indices, 10] <= 0)
est36 <- mean(quantity[indices, 11] <= 0)
est37 <- mean(quantity[indices, 12] <= 0)
est38 <- mean(quantity[indices, 13] <= 0)
est39 <- mean(quantity[indices, 14] <= 0)
# TOJ estimate
tojest <- 3.536 * est -
4.072 * (est21 + est22 + est23 + est24) / 4 +
1.536 * (est31 + est32 + est33 + est34 +
est35 + est36 + est37 + est38 + est39) / 9
# Ensure valid estimates
tojest <- ifelse(tojest >= 0, tojest, 0)
tojest <- ifelse(tojest <= 1, tojest, 1)
return(tojest)
}
#' Compute bootstrap TOJ empirical CDF estimate for T equivalent to 2 modulo 6
#'
#' @param quantity An N * 12 matrix of estimates
#' @param indices A vector of indices for bootstrap repetitions
#'
#' @noRd
#'
toj2_boot <- function(quantity, indices) {
# Estimates
est <- mean(quantity[indices, 1] <= 0)
est21 <- mean(quantity[indices, 2] <= 0)
est22 <- mean(quantity[indices, 3] <= 0)
est31 <- mean(quantity[indices, 4] <= 0)
est32 <- mean(quantity[indices, 5] <= 0)
est33 <- mean(quantity[indices, 6] <= 0)
est34 <- mean(quantity[indices, 7] <= 0)
est35 <- mean(quantity[indices, 8] <= 0)
est36 <- mean(quantity[indices, 9] <= 0)
est37 <- mean(quantity[indices, 10] <= 0)
est38 <- mean(quantity[indices, 11] <= 0)
est39 <- mean(quantity[indices, 12] <= 0)
# TOJ estimate
tojest <- 3.536 * est -
4.072 * (est21 + est22) / 2 +
1.536 * (est31 + est32 + est33 + est34 +
est35 + est36 + est37 + est38 + est39) / 9
# Ensure valid estimates
tojest <- ifelse(tojest >= 0, tojest, 0)
tojest <- ifelse(tojest <= 1, tojest, 1)
return(tojest)
}
#' Compute bootstrap TOJ empirical CDF estimate for T equivalent to 3 modulo 6
#'
#' @param quantity An N * 8 matrix of estimates
#' @param indices A vector of indices for bootstrap repetitions
#'
#' @noRd
#'
toj3_boot <- function(quantity, indices) {
# Estimates
est <- mean(quantity[indices, 1] <= 0)
est21 <- mean(quantity[indices, 2] <= 0)
est22 <- mean(quantity[indices, 3] <= 0)
est23 <- mean(quantity[indices, 4] <= 0)
est24 <- mean(quantity[indices, 5] <= 0)
est31 <- mean(quantity[indices, 6] <= 0)
est32 <- mean(quantity[indices, 7] <= 0)
est33 <- mean(quantity[indices, 8] <= 0)
# TOJ estimate
tojest <- 3.536 * est -
4.072 * (est21 + est22 + est23 + est24) / 4 +
1.536 * (est31 + est32 + est33) / 3
# Ensure valid estimates
tojest <- ifelse(tojest >= 0, tojest, 0)
tojest <- ifelse(tojest <= 1, tojest, 1)
return(tojest)
}
#' Compute bootstrap TOJ empirical CDF estimate for T equivalent to 4 modulo 6
#'
#' @param quantity An N * 12 matrix of estimates
#' @param indices A vector of indices for bootstrap repetitions
#'
#' @noRd
#'
toj4_boot <- function(quantity, indices) {
# Estimates
est <- mean(quantity[indices, 1] <= 0)
est21 <- mean(quantity[indices, 2] <= 0)
est22 <- mean(quantity[indices, 3] <= 0)
est31 <- mean(quantity[indices, 4] <= 0)
est32 <- mean(quantity[indices, 5] <= 0)
est33 <- mean(quantity[indices, 6] <= 0)
est34 <- mean(quantity[indices, 7] <= 0)
est35 <- mean(quantity[indices, 8] <= 0)
est36 <- mean(quantity[indices, 9] <= 0)
est37 <- mean(quantity[indices, 10] <= 0)
est38 <- mean(quantity[indices, 11] <= 0)
est39 <- mean(quantity[indices, 12] <= 0)
# TOJ estimate
tojest <- 3.536 * est -
4.072 * (est21 + est22) / 2 +
1.536 * (est31 + est32 + est33 + est34 +
est35 + est36 + est37 + est38 + est39) / 9
# Ensure valid estimates
tojest <- ifelse(tojest >= 0, tojest, 0)
tojest <- ifelse(tojest <= 1, tojest, 1)
return(tojest)
}
#' Compute bootstrap TOJ empirical CDF estimate for T equivalent to 5 modulo 6
#'
#' @param quantity N * 14 matrix of estimates
#' @param indices A vector of indices for bootstrap repetitions
#'
#' @noRd
#'
toj5_boot <- function(quantity, indices) {
# Estimates
est <- mean(quantity[indices, 1] <= 0)
est21 <- mean(quantity[indices, 2] <= 0)
est22 <- mean(quantity[indices, 3] <= 0)
est23 <- mean(quantity[indices, 4] <= 0)
est24 <- mean(quantity[indices, 5] <= 0)
est31 <- mean(quantity[indices, 6] <= 0)
est32 <- mean(quantity[indices, 7] <= 0)
est33 <- mean(quantity[indices, 8] <= 0)
est34 <- mean(quantity[indices, 9] <= 0)
est35 <- mean(quantity[indices, 10] <= 0)
est36 <- mean(quantity[indices, 11] <= 0)
est37 <- mean(quantity[indices, 12] <= 0)
est38 <- mean(quantity[indices, 13] <= 0)
est39 <- mean(quantity[indices, 14] <= 0)
# TOJ estimate
tojest <- 3.536 * est -
4.072 * (est21 + est22 + est23 + est24) / 4 +
1.536 * (est31 + est32 + est33 + est34 +
est35 + est36 + est37 + est38 + est39) / 9
# Ensure valid estimates
tojest <- ifelse(tojest >= 0, tojest, 0)
tojest <- ifelse(tojest <= 1, tojest, 1)
return(tojest)
}
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