R/psiFunctions.R

In saeRobust: Robust Small Area Estimation

#' psiOne
#'
#' @description \code{psiOne} is a Huber influence function. \code{getK}
#'   function to compute capital K -- used internally.
#'
#' @param u standardized residuals
#' @param k tuning constant
#' @param deriv if \code{TRUE} returns the derivative
#'
#' @rdname psiFunctions
#' @export
#'
#' @examples
#' set.seed(1)
#' u <- rnorm(10)
#' psiOne(u, k = 1.345, deriv = FALSE)
psiOne <- function(u, k = 1.345, deriv = FALSE){
    u <- as.numeric(u) # in the case that u comes from the Matrix package
    if (deriv) return(as.numeric(abs(u) <= k))

    # commented out is the influence function used by Tzavidis (2005) - M-Quantile
    # sm <- median(abs(u)) / 0.6745
    # w <- pmin(1, k / abs(u / sm))
    # w * u

    u * pmin(1, k / abs(u))
}

#' @rdname psiFunctions
#' @export
getK <- function(k) {
    2 * pnorm(k) - 1 - 2 * k * dnorm(k) + 2 * (k^2) * (1 - pnorm(k))
}