#' GEVr Shape Parameter Profile Likelihood Estimation for Stationary Models
#'
#' Computes the profile likelihood based confidence interval for the shape parameter of the stationary GEVr model.
#'
#' @param z A class object returned from gevrFit.
#' @param conf Confidence level to use. Defaults to 95 percent.
#' @param plot Plot the profile likelihood and estimate (vertical line)?
#' @param opt Optimization method to maximize the profile likelihood, passed to optim. The default method is Nelder-Mead.
#'
#' @examples
#' ## Compare the length of the shape confidence intervals using GEV1 vs. GEV10
#' set.seed(7)
#' x <- rgevr(200, 10, loc = 0.5, scale = 1, shape = -0.3)
#' z1 <- gevrFit(x[, 1])
#' z2 <- gevrFit(x)
#' gevrProfShape(z1)
#' gevrProfShape(z2)
#' @return
#' \item{Estimate}{Estimated shape parameter.}
#' \item{CI}{Profile likelihood based confidence interval for the shape parameter.}
#' \item{ConfLevel}{The confidence level used.}
#' @export
gevrProfShape <- function(z, conf = .95, plot = TRUE, opt = c("Nelder-Mead")) {
if(z$gumbel | !z$stationary)
stop("Object cannot be from a Gumbel and/or a nonstationary fit!")
data <- as.matrix(z$data)
theta <- as.numeric(z$par.ests)
opt <- match.arg(opt)
sol <- c(theta[1], theta[2])
gevrLikShape <- function(a, sh) {
if(a[2] <= 0) {
out <- .Machine$double.xmax
} else {
out <- dgevr(data, loc = a[1], scale = a[2], shape = sh, log.d = TRUE)
out <- - sum(out)
if(out == Inf)
out <- .Machine$double.xmax
}
out
}
cutoff <- qchisq(conf, 1)
prof <- function(sh) {
lmax <- dgevr(data, theta[1], theta[2], theta[3], log.d = TRUE)
lmax <- sum(lmax)
yes <- optim(sol, gevrLikShape, method = opt, sh = sh)
sol <- yes$par
lci <- -yes$value
2*(lmax-lci) - cutoff
}
prof <- Vectorize(prof)
suppressWarnings(out1 <- uniroot(prof, c(theta[3] - 1e-6, theta[3]), extendInt="downX"))
suppressWarnings(out2 <- uniroot(prof, c(theta[3], theta[3] + 1e-6), extendInt="upX"))
CI <- c(min(out1$root, out2$root), max(out1$root, out2$root))
if(plot) {
prof1 <- function(sh) {- prof(sh)}
curve(prof1, from = CI[1], to = CI[2], n = 50, xlab = 'Shape', ylab = 'LRT - Cutoff')
abline(v = theta[3], col = "blue")
}
out <- list(theta[3], CI, conf)
names(out) <- c("Estimate", "CI", "ConfLevel")
out
}
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.