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#' Studentized Residuals for Rank-Based Regression
#'
#' Returns the Studentized residuals based on rank-based estimation.
#'
#'
#' @param model an object of class rfit
#' @param \dots additional arguments. currently not used.
#' @author John Kloke
#' @seealso \code{\link{rfit}}
#' @references Hettmansperger, T.P. and McKean J.W. (2011), \emph{Robust
#' Nonparametric Statistical Methods, 2nd ed.}, New York: Chapman-Hall.
#' @examples
#'
#' x<-runif(47)
#' y<-rcauchy(47)
#' qqnorm(rstudent(fit<-rfit(y~x)))
#' plot(x,rstudent(fit)) ; abline(h=c(-2,2))
#'
#' @export rstudent.rfit
"rstudent.rfit" <- function (model,...) {
fit<-model
ehat <- fit$resid
n <- length(ehat)
p <- fit$qrx1$rank-1
sigmahat <- mad(ehat)
deltas <- sum(abs(ehat))/(n - p)
# delta <- disp(fit$betahat, fit$x, fit$y, fit$scores)/(n - p)
delta <- model$D1/(n - p)
k2 <- (fit$tauhat/sigmahat)^2 * (2 * delta/fit$tauhat - 1)
if (fit$symmetric) {
h <- hat(fit$x)
s <- suppressWarnings(sigmahat * sqrt(1 - k2 * h))
s[is.na(s)] <- sigmahat * sqrt(1 - h)[is.na(s)]
} else {
hc <- hat(as.matrix(qr.Q(fit$qrx1)[,2:(p+1)]), intercept=FALSE)
k1 <- (fit$taushat/sigmahat)^2 * (2 * deltas/fit$taushat - 1)
s <- suppressWarnings(sigmahat * sqrt(1 - k1/n - k2 * hc))
s[is.na(s)] <- sigmahat * sqrt(1 - hc)[is.na(s)]
}
ehat/s
}
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