# ----------------------------------------
# Authors: Josef Holzer and Andreas Alfons
#          Vienna University of Technology
# ----------------------------------------

thetaISE <- function(x, k, ...) {
    ## initializations
    if(!is.numeric(x) || length(x) == 0) stop("'x' must be a numeric vector")
    if(!is.numeric(k) || length(k) == 0 || k[1] < 1) {
        stop("'k' must be a positive integer")
    } else k <- k[1]
    if(any(i <- is.na(x))) x <- x[!i]  # remove missing values
    x <- sort(x)
    n <- length(x)
    if(k >= n) stop("'k' must be smaller than the number of observed values")
    x0 <- x[n-k]  # threshold (scale parameter)
    y <- x[(n-k+1):n]/x0  # relative excesses
    ## integrated squared error distance criterion
    ISE <- function(theta, y, k) {
        f <- theta*y^(-1-theta)
        theta^2/(2*theta+1) - 2*sum(f)/k
    }
    ## minimize
    localNlm <- function(f, p = NULL, ...) {
        if(is.null(p)) p <- thetaHill(x, k)  # starting parameter
        nlm(f, p, ...)
    }
    localNlm(ISE, y=y, k=k, ...)$estimate
}