RTDE (version 0.2-0)

fitRTDE: Fitting a Tail Dependence model with a Robust Estimator

Description

Fit a Tail Dependence model with a Robust Estimator.

Usage

fitRTDE(obs, nbpoint, alpha, omega, method="MDPDE", fix.arg=list(rho=-1),
    boundary.method="log", control=list())

# S3 method for fitRTDE
print(x, …)
# S3 method for fitRTDE
summary(object, …)
# S3 method for fitRTDE
plot(x, which=1:2, main, …)

Arguments

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 "MDPDE".

fix.arg

a named list of fixed arguments: either \(rho\) only e.g. list(rho=-1) or \(rho, delta\) e.g. list(rho=-1, delta=0).

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 "fitRTDE".

…

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.

Value

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.

Details

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") .

References

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).

Examples

# NOT RUN {
#####
# (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)


# }