R/calcDepth.R

In melaniehorn/GSignTest: Robust Tests for Regression-Parameters via Sign Depth

#' @title Calculating the K-sign depth
#'
#' @description
#' \code{calcDepth} calculates the K-sign depth of a given
#' vector of residuals.
#'
#' @param res [\code{numeric}]\cr
#'   numeric vector of residuals
#' @param K [\code{integer(1)}]\cr
#'   the parameter K for the sign depth
#' @param transform [\code{logical(1)}]\cr
#'   Should the depth be transformed by the formula \eqn{N * (res - 0.5^(K-1))},
#'   so that the distribution of the K-sign depth converges for large number
#'   of data points N? Default is \code{FALSE}.
#' @return [\code{numeric(1)}] the calculated K-sign depth of \code{res}.
#'
#' @note The implementation is based on a work of Dennis Malcherczyk.
#'
#' @references
#' Malcherczyk, D. (2021+). K-sign depth: Asymptotic distribution, efficient
#' computation and applications. Dissertation in preparation.
#'
#'
#' @examples
#' calcDepth(rnorm(10), 3)
#' calcDepth(runif(100, -1, 1), 4, transform = TRUE)
#' @export
calcDepth <- function(res, K, transform = FALSE) {
  assert_numeric(res, min.len = K, any.missing = FALSE)
  assert_integerish(K, lower = 2, len = 1, any.missing = FALSE)
  assert_logical(transform, any.missing = FALSE, len = 1)

  res2 <- res[res != 0]
  N <- length(res)
  M <- length(res2)

  signRes <- sign(res2)
  if (transform) {
    return((RcppCalcKDepthBlock(signRes, K = K) / choose(M, K) - (1/2)^(K-1)) * M)
  } else {
    return(RcppCalcKDepthBlock(signRes, K = K) / choose(M, K))
  }
  if (M != N) {
    erg <- (choose(M, K) * erg + choose(N - M, K)) / choose(N, K)
  }
  return(erg)
}