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#' @export
#'
#' @references Srivastava, M. S. (2005). Some Tests Concerning the
#' Covariance Matrix in High Dimensional Data. Journal of the Japan
#' Statistical Society, 35(2), 251-272. \href{http://doi.org/10.14490/jjss.35.251}{10.14490/jjss.35.251}
#' @rdname structureStatistics
Srivastava2005 <- function(x, Sigma = "identity", ...){
UseMethod("Srivastava2005")
}
#' @export
#' @keywords internal
#' @importFrom stats pchisq
#'
Srivastava2005.covariance <- function(x, Sigma = "identity", ...){
p <- ncol(x)
n <- attributes(x)$df + 1
S <- x
if(Sigma[[1]] == "identity"){
S_ <- x
}else{
svCov <- svd(x)
sv <- svd(Sigma)
x_ <- svCov$u %*% diag(sqrt(svCov$d)) %*%
solve(sv$u %*% diag(sqrt(sv$d)))
S_ <- t(x_) %*% x_
}
statistic <- Srivastava2005Stat(S_)
names(statistic) <- "Standard Normal"
parameter <- c(0, 1)
names(parameter) <- c("Mean", "Variance")
null.value <- 0
names(null.value) <- "difference between the Sample \nCovariance Matrix and the Null Covariance Matrix Structure\n"
p.value <- 1 - pnorm(abs(statistic))
estimate <- S
estimate <- if(nrow(estimate) > 5){
NULL
}else{
estimate
}
obj <- list(statistic = statistic,
parameter = parameter,
p.value = p.value,
estimate = estimate,
null.value = null.value,
alternative = "two.sided",
method = "Srivastava 2005 Test of Covariance Matrix Structure")
class(obj) <- "htest"
obj
}
#' @export
#' @keywords internal
#' @importFrom stats cov
#' @importFrom stats pchisq
#'
Srivastava2005.matrix <- function(x, Sigma = "identity", ...){
p <- ncol(x)
n <- nrow(x)
S <- cov(x)
if(Sigma[[1]] == "identity"){
S_ <- S
}else{
sv <- svd(Sigma)
svDf <- svd(S)
x_ <- svDf$u %*% diag(sqrt(sv$d)) %*% solve(sv$u %*% diag(sqrt(sv$d)))
S_ <- t(x_) %*% x_
}
statistic <- Srivastava2005Stat(S_)
names(statistic) <- "Standard Normal"
parameter <- c(0, 1)
names(parameter) <- c("Mean", "Variance")
null.value <- 0
names(null.value) <- "difference between the Sample \nCovariance Matrix and the Null Covariance Matrix Structure\n"
p.value <- 1 - pnorm(abs(statistic))
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 = "Srivastava 2005 Test of Covariance Matrix Structure")
class(obj) <- "htest"
obj
}
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