#' @export
#'
#' @references Nagao, H. (1973). On Some Test Criteria for Covariance
#' Matrix. The Annals of Statistics, 1(4), 700-709
#' @rdname structureStatistics
Nagao1973 <- function(x, Sigma = "identity", ...){
UseMethod("Nagao1973")
}
#' @export
#' @keywords internal
#' @importFrom stats pchisq
#'
Nagao1973.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$d)))
S_ <- t(x_) %*% x_
}
statistic <- Nagao1973_(n, p, S_)
names(statistic) <- "Chi Squared"
parameter <- p * (p + 1) / 2
names(parameter) <- "df"
null.value <- 0
names(null.value) <- "difference between the Sample Covariance Matrix and the Null Covariance Matrix Structure"
p.value <- 1 - pchisq(statistic, parameter)
estimate <- S
estimate <- if(nrow(estimate) > 5){
NULL
}else{
estimate
}
obj <- list(statistic = statistic,
parameter = parameter,
p.value = p.value,
estimate = estimate,
null.value = null.value,
alternative = "two.sided",
method = "Nagao 1973 Test of Covariance Matrix Structure")
class(obj) <- "htest"
obj
}
#' @export
#' @keywords internal
#' @importFrom stats cov
#' @importFrom stats pchisq
#'
Nagao1973.matrix <- function(x, Sigma = "identity", ...){
p <- ncol(x)
n <- nrow(x)
S <- cov(x)
if(Sigma[[1]] == "identity"){
S_ <- S
}else{
sv <- svd(Sigma)
svDf <- svd(S)
x_ <- svDf$u %*% diag(sqrt(sv$d)) %*% solve(sv$u %*% diag(sqrt(sv$d)))
S_ <- t(x_) %*% x_
}
statistic <- Nagao1973_(n, p, S_)
names(statistic) <- "Chi Squared"
parameter <- p * (p + 1) / 2
names(parameter) <- "df"
null.value <- 0
names(null.value) <- "difference between the Sample Covariance Matrix and the Null Covariance Matrix Structure"
p.value <- 1 - pchisq(statistic, parameter)
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 = "Nagao 1973 Test of Covariance Matrix Structure")
class(obj) <- "htest"
obj
}
#' @keywords internal
Nagao1973_ <- function(n, p, S_){
mid <- S_ - diag(1, p)
n * p * (tr(mid %*% mid) / p) / 2
}
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.