fitRTDE | R Documentation |
Fit a Tail Dependence model with a Robust Estimator.
fitRTDE(obs, nbpoint, alpha, omega, method="MDPDE", fix.arg=list(rho=-1),
boundary.method="log", control=list())
## S3 method for class 'fitRTDE'
print(x, ...)
## S3 method for class 'fitRTDE'
summary(object, ...)
## S3 method for class 'fitRTDE'
plot(x, which=1:2, main, ...)
obs |
bivariate numeric dataset. |
nbpoint |
a numeric for the number of largest points to be selected. |
alpha |
a numeric for the power divergence parameter. |
omega |
a numeric for omega, see section Details. |
method |
a character string equals to |
fix.arg |
a named list of fixed arguments:
either |
boundary.method |
a character string: either "log" or "simple", see section Details. |
control |
A list of control paremeters. See section Details. |
x , object |
an R object inheriting from |
... |
arguments to be passed to subsequent methods. |
which |
an integer (1 or 2) to specify whether to plot eta or delta, respectively. |
main |
a main title for the plot. |
The function fitRTDE
fits an extended Pareto distribution
(\eta,\tau
are fitted while \rho
is fixed)
on the relative excess of Z_\omega
(see zvalueRTDE
)
using a robust estimator based on the minimum distance power
divergence criterion (see MDPD
).
The boundary enforcement on \eta,\tau
is either done
by the bounded BFGS algorithm (see optim
with
method="L-BFGS-B"
) or by the bounded Nelder-Mead
algorithm (see constrOptim
with
method="Nelder-Mead"
) .
fitRTDE
returns an object of class "fitRTDE"
having the following components:
n
rownumber of data
.
n0
rownumber of contamin
.
alpha
a vector of alpha
parameters.
omega
a vector of omega
parameters.
m
a vector of nbpoint
.
rho
a numeric for rho
.
eta
estimate of eta
.
delta
estimate of delta
.
Ztilde
see zvalueRTDE
.
Christophe Dutang
C. Dutang, Y. Goegebeur, A. Guillou (2014), Robust and bias-corrected estimation of the coefficient of tail dependence, Volume 57, Insurance: Mathematics and Economics
This work was supported by a research grant (VKR023480) from VILLUM FONDEN and an international project for scientific cooperation (PICS-6416).
#####
# (1) simulation
omega <- 1/2
m <- 48
n <- 100
obs <- cbind(rupareto(n), rupareto(n)) + rupareto(n)
#function of m
system.time(
x <- fitRTDE(obs, nbpoint=m:(n-m), 0, 1/2)
)
x
summary(x)
plot(x, which=1)
plot(x, which=2)
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