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#' Choose the Tuning Parameter of the Ridge Inverse and
#' Thresholding Level of the Empirical p-Values
#'
#' Choose the tuning parameter of the ridge inverse and p-value cutoff by
#' minimizing cross validation estimates of the total prediction errors of
#' the p separate ridge regressions.
#'
#' @param x n by p data matrix.
#' @param lambda A vector of candidate tuning parameters.
#' @param pcut A vector of candidate cutoffs of pvalues.
#' @param fold fold-cross validation is performed.
#'
#' @returns The total prediction errors for all lambda (row-wise) and pcut
#' (column-wise)
#'
#' @references
#' Ha, M. J. and Sun, W.
#' (2014).
#' Partial correlation matrix estimation using ridge penalty followed by
#' thresholding and re-estimation.
#' Biometrics, 70, 762--770.
#'
#' @author Min Jin Ha
#'
#' @examples
#' p <- 100 # number of variables
#' n <- 50 # sample size
#'
#' ###############################
#' # Simulate data
#' ###############################
#' simulation <- simulateData(G = p, etaA = 0.02, n = n, r = 1)
#' data <- simulation$data[[1L]]
#' stddata <- scale(x = data, center = TRUE, scale = TRUE)
#'
#' ###############################
#' # Selection of a lambda and a
#' # p-value cutoff
#' ###############################
#' lambda.array <- seq(from = 0.1, to = 5, length = 10) * (n-1.0)
#' pcut.array <- seq(from = 0.01, to = 0.05, by = 0.01)
#' tpe <- lambda.pcut.cv(x = stddata,
#' lambda = lambda.array,
#' pcut = pcut.array,
#' fold = 3L)
#' w.mintpe <- which(tpe == min(tpe), arr.ind = TRUE)
#' lambda <- lambda.array[w.mintpe[1L]]
#' alpha <- pcut.array[w.mintpe[2L]]
#'
#' @include lambda.pcut.cv1.R splitSets.R
#' @export
lambda.pcut.cv <- function(x, lambda, pcut, fold = 10L) {
n <- nrow(x)
cv <- 1L:n %% fold + 1L
cv <- cbind(cv, sample(1:n))
PE <- matrix(0.0,
nrow = length(lambda),
ncol = length(pcut),
dimnames = list(lambda, pcut))
k <- length(lambda)
message("cv: ", appendLF = FALSE)
for (i in 1L:fold) {
message(i, " ", appendLF = FALSE)
sets <- splitSets(cv = cv, i = i, x = x)
PE <- PE + lambda.pcut.cv1(train = sets$train,
test = sets$test,
lambda = lambda,
pcut = pcut)
}
message("Done!")
PE / fold
}
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