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#############################################################################
# Copyright (c) 2014 Mathieu Ribatet
#
# This program is free software; you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation; either version 2 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program; if not, write to the
# Free Software Foundation, Inc.,
# 59 Temple Place, Suite 330, Boston, MA 02111-1307, USA
#
#############################################################################
fitpp <- function(data, threshold, noy = length(data) / 365.25, start, ...,
std.err.type = "observed", corr = FALSE,
method = "BFGS", warn.inf = TRUE){
if (all(c("observed", "none") != std.err.type))
stop("``std.err.type'' must be one of 'observed' or 'none'")
std.err.type <- match.arg(std.err.type, c("observed", "none"))
nlpp <- function(loc, scale, shape) {
-.C(POT_do_pplik, exceed, nat, loc, scale, shape,
threshold, noy, dns = double(1))$dns
}
noy <- as.double(noy)
nn <- length(data)
high <- (data > threshold) & !is.na(data)
threshold <- as.double(threshold)
exceed <- as.double(data[high])
nat <- as.integer(length(exceed))
if(!nat)
stop("no data above threshold")
pat <- nat/nn
param <- c("loc", "scale", "shape")
if(missing(start)) {
start <- list(loc = 0, scale = 0, shape = 0)
start$scale <- sqrt(6 * var(exceed))/pi
start$loc <- mean(exceed) + (log(noy) - 0.58) * start$scale
start <- start[!(param %in% names(list(...)))]
}
if(!is.list(start))
stop("`start' must be a named list")
if(!length(start))
stop("there are no parameters left to maximize over")
nm <- names(start)
l <- length(nm)
f <- formals(nlpp)
names(f) <- param
m <- match(nm, param)
if(any(is.na(m)))
stop("`start' specifies unknown arguments")
formals(nlpp) <- c(f[m], f[-m])
nllh <- function(p, ...) nlpp(p, ...)
if(l > 1)
body(nllh) <- parse(text = paste("nlpp(", paste("p[",1:l,
"]", collapse = ", "), ", ...)"))
fixed.param <- list(...)[names(list(...)) %in% param]
if(any(!(param %in% c(nm,names(fixed.param)))))
stop("unspecified parameters")
start.arg <- c(list(p = unlist(start)), fixed.param)
if( warn.inf && do.call("nllh", start.arg) == 1e6 )
warning("negative log-likelihood is infinite at starting values")
opt <- optim(start, nllh, hessian = TRUE, ..., method = method)
if ((opt$convergence != 0) || (opt$value == 1e6)) {
warning("optimization may not have succeeded")
if(opt$convergence == 1) opt$convergence <- "iteration limit reached"
}
else opt$convergence <- "successful"
tol <- sqrt(.Machine$double.eps)
if(std.err.type == "observed") {
var.cov <- qr(opt$hessian, tol = tol)
if(var.cov$rank != ncol(var.cov$qr)){
warning("observed information matrix is singular.")
std.err.type <- "none"
std.err <- corr.mat <- var.cov <- NULL
}else
{
var.cov <- structure(solve(var.cov, tol = tol), dimnames = list(nm,nm))
std.err <- diag(var.cov)
names(std.err) <- nm
if(any(std.err <= 0)){
warning("observed information matrix has non positive diagonal terms.")
std.err.type <- "none"
std.err <- corr.mat <- var.cov <- NULL
}else
{
std.err <- sqrt(std.err)
if(corr)
{
.mat <- diag(1/std.err, nrow = length(std.err))
corr.mat <- structure(.mat %*% var.cov %*% .mat,
dimnames = list(nm,nm))
diag(corr.mat) <- rep(1, length(std.err))
}else
{
corr.mat <- NULL
}
}
}
}else # if(std.err.type == "none")
std.err <- corr.mat <- var.cov <- NULL
param <- c(opt$par, unlist(fixed.param))
##Transform the point process parameter to the GPD ones
scale <- param["scale"] + param["shape"] *
(threshold - param["loc"])
var.thresh <- !all(threshold == threshold[1])
if (!var.thresh)
threshold <- threshold[1]
fitted <- list(fitted.values = opt$par, std.err = std.err, std.err.type = std.err.type,
var.cov = var.cov, fixed = unlist(fixed.param), param = param,
deviance = 2*opt$value, corr = corr.mat, convergence = opt$convergence,
counts = opt$counts, message = opt$message, threshold = threshold,
nat = nat, pat = pat, data = data, exceed = exceed, scale = scale,
var.thresh = var.thresh, est = "MLE", logLik = -opt$value,
opt.value = opt$value)
fitted$threshold.call <- deparse(threshold)
class(fitted) <- c("uvpot","pot")
return(fitted)
}
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