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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
#
#############################################################################
## 8) Likelihood Moment Estimator
##Likelihood moment estimation
gpdlme <- function(x, threshold, r = -.5, start, ...,
method = "BFGS"){
nn <- length(x)
high <- (x > threshold) & !is.na(x)
exceed <- as.double(x[high])
nat <- length(exceed)
if (!nat)
stop("no data above threshold")
pat <- nat/nn
excess <- exceed - threshold
fun <- function(x){
if (x >= 1/max(excess))
return(1e6)
p <- r / mean(log(1 - x * excess))
abs(mean((1 - x * excess)^p) - 1 / (1 - r))
}
if (missing(start))
start <- list(x = -1)
opt <- optim(start, fun, hessian = TRUE, ..., method = method)
if (opt$convergence != 0){
warning("optimization may not have succeeded")
if(opt$convergence == 1) opt$convergence <- "iteration limit reached"
}
else opt$convergence <- "successful"
counts <- opt$counts
b <- opt$par
zero <- opt$value
shape <- mean(log(1 - b*excess))
scale <- - shape / b
param <- c(scale, shape)
names(param) <- c("scale", "shape")
a11 <- scale^2 * (2 + ((r - shape)^2 + 2 * shape) /
(1 - 2 * r))
a12 <- scale * (1 + (r^2 + shape^2 + shape) /
(1 - 2 * r))
a22 <- (1 - r) * (1 + (2*shape^2 - 2 * shape + r) /
(1 - 2 * r))
var.cov <- matrix(c(a11, a12, a12, a22), 2) / nat
colnames(var.cov) <- c("scale", "shape")
rownames(var.cov) <- c("scale", "shape")
std.err <- sqrt(diag(var.cov))
.mat <- diag(1/std.err, nrow = length(std.err))
corr <- structure(.mat %*% var.cov %*% .mat)
diag(corr) <- rep(1, length(std.err))
colnames(corr) <- c("scale", "shape")
rownames(corr) <- c("scale", "shape")
if (shape < -0.5)
message <- "Assymptotic theory assumptions\nfor standard error may not be fullfilled !"
else message <- NULL
var.thresh <- FALSE
return(list(fitted.values = param, std.err = std.err, std.err.type = "expected",
var.cov = var.cov, param = param, message = message, data = x,
threshold = threshold, corr = corr, convergence = opt$convergence,
counts = counts, nat = nat, pat = pat, exceed = exceed, scale = scale,
var.thresh = var.thresh, est = "LME", opt.value = opt$value))
}
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