#' @export
#'
#' @references Ahmad, M. R. and Rosen, D. von. (2015). Tests for
#' High-Dimensional Covariance Matrices Using the Theory of U-statistics.
#' Journal of Statistical Computation and Simulation, 85(13), 2619-2631.
#' \href{http://doi.org/10.1080/00949655.2014.948441}{10.1080/00949655.2014.948441}
#' @rdname structureStatistics
Ahmad2015 <- function(x, Sigma = "identity", ...){
UseMethod("Ahmad2015")
}
#' @export
#' @keywords internal
#' @importFrom stats pnorm
#'
Ahmad2015.covariance <- function(x, Sigma = "identity", ...){
p <- ncol(x)
n <- attributes(x)$df + 1
S <- x
if(Sigma[[1]] == "identity"){
svCov <- svd(x)
x_ <- svCov$u %*% diag(sqrt(svCov$d))
}else{
svCov <- svd(x)
sv <- svd(Sigma)
x_ <- svCov$u %*% diag(sqrt(svCov$d)) %*%
solve(sv$u %*% diag(sqrt(sv$d)))
}
statistic <- Ahmad2015Stat(x_)
names(statistic) <- "Normal"
parameter <- c(0, 4 * (2 / (p / n + 1)))
names(parameter) <- c("Mean", "Variance")
null.value <- 0
names(null.value) <- "difference between the Sample Covariance Matrix and the Null Covariance Matrix Structure"
p.value <- 1 - pnorm(abs(statistic), 0, 4 * (2 / (p / n + 1)))
estimate <- S
estimate <- if(nrow(estimate) > 5){
NULL
}else{
estimate
}
obj <- list(statistic = statistic,
parameter = parameter,
p.value = p.value,
estimate = estimate,
null.value = null.value,
alternative = "two.sided",
method = "Ahmad and Rosen 2015 Test of Covariance Matrix Structure")
class(obj) <- "htest"
obj
}
#' @export
#' @keywords internal
#' @importFrom stats cov
#' @importFrom stats pnorm
#'
Ahmad2015.matrix <- function(x, Sigma = "identity", ...){
p <- ncol(x)
n <- nrow(x)
S <- cov(x)
if(Sigma[[1]] == "identity"){
x_ <- x
}else{
sv <- svd(Sigma)
x_ <- x %*% solve(sv$u %*% diag(sqrt(sv$d)))
}
statistic <- Ahmad2015Stat(x_)
names(statistic) <- "Normal"
parameter <- c(0, 4 * (2 / (p / n + 1)))
names(parameter) <- c("Mean", "Variance")
null.value <- 0
names(null.value) <- "difference between the Sample Covariance Matrix and the Null Covariance Matrix Structure"
p.value <- 1 - pnorm(abs(statistic), 0, 4 * (2 / (p / n + 1)))
estimate <- S
estimate <- if(nrow(estimate) > 5){
NULL
}else{
estimate
}
obj <- list(statistic = statistic,
parameter = parameter,
p.value = p.value,
estimate = estimate,
null.value = null.value,
alternative = "two.sided",
method = "Ahmad and Rosen 2015 Test of Covariance Matrix Structure")
class(obj) <- "htest"
obj
}
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