kdecvine: Kernel density estimatior based on simplified C-vine copulas

In tvatter/eecop: Copula-based solutions to moment equations

Description

Implements the C-vine based estimator of Nagler and Czado (2016). We refer to kdevine for more details.

Usage

kdecvine(x, y, mult_1d = 1, xmin = NULL, xmax = NULL, ...)

Arguments

x	(n x (d-1)) data matrix.
y	(n x 1) data vector for the central node.
mult_1d	numeric; all bandwidhts for marginal kernel density estimation are multiplied with mult_1d. Defaults to log(1 + d).
xmin	numeric vector of length d; see kde1d.
xmax	numeric vector of length d; see kde1d.
...	further arguments passed to kde1d or kdevinecop.

Value

An object of class kdecvine.

Author(s)

Thibault Vatter

References

Nagler, T., Czado, C. (2016) Evading the curse of dimensionality in nonparametric density estimation with simplified vine copulas. Journal of Multivariate Analysis 151, 69-89 (doi:10.1016/j.jmva.2016.07.003)

See Also

dkdecvine kdevine kdevine

Examples

set.seed(0)

# Quantiles of interest
alpha <- c(0.1,0.5,0.9)

## The predictors
p <- 10
n <- 1e3
X <- matrix(2 * runif(n * p) - 1, n, p)
colnames(X) <- paste0("X", 1:p)

## mean and variance shifts
Y1 <- rnorm(n) + exp(X[,1])
Y2 <- rnorm(n) * (1 + exp(X[,1]))

## For the evaluation of the results
ticks = 1e2
X.test = matrix(0, ticks, p)
X.test[,1] = seq(-0.9, 0.9, length.out = ticks)
colnames(X.test) <- paste0("X", 1:p)

## The truth
truth1 <- cbind(qnorm(0.1) + exp(X.test[,1]),
                exp(X.test[,1]),
                qnorm(0.9) + exp(X.test[,1]))
truth2 <- cbind(qnorm(0.1) * (1 + exp(X.test[,1])),
                0,
                qnorm(0.9) * (1 + exp(X.test[,1])))

## range for the margin estimates
xmin <- c(-Inf,rep(-1, p))
xmax <- c(Inf,rep(1, p))

## Can we identify the right structure?
rvr1 <- kdecvine(x = X, y = Y1, xmin = xmin, xmax = xmax,
                 test.level = 0.05, trunc.level = 1, treecrit = "hoeffd")
rvr2 <- kdecvine(x = X, y = Y2, xmin = xmin, xmax = xmax,
                 test.level = 0.05, trunc.level = 1, treecrit = "hoeffd")

## Quantile regression results
rq1 <- predict(rvr1, X.test, "quantile", tau = c(0.1, 0.5, 0.9))
rq2 <- predict(rvr2, X.test, "quantile", tau = c(0.1, 0.5, 0.9))

## Plot the results
par(mfrow = c(1,2))
plot(X[,1], Y1, xlab = "X1", ylab = "Y1")
matlines(X.test[,1], truth1, col = "green", lty = c(2,1,2), lwd = 2)
matlines(X.test[,1], rq1, col = "red", lty = c(2,1,2), lwd = 2)
legend("topleft", legend = c("data", "truth", "estimate"),
       col = c(1, "green", "red"),
       pch = c(1, rep(NA,2)),
       lty = c(0, rep(1,2)),
       cex = 0.7)
plot(X[,1], Y2, xlab = "X1", ylab = "Y2")
matlines(X.test[,1], truth2, col = "green", lty = c(2,1,2), lwd = 2)
matlines(X.test[,1], rq2, col = "red", lty = c(2,1,2), lwd = 2)

tvatter/eecop documentation built on May 28, 2019, 7:52 a.m.