fitRTDE {RTDE}

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 class 'fitRTDE'
print(x, ...)
## S3 method for class 'fitRTDE'
summary(object, ...)
## S3 method for class '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.

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") .

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.

Author(s)

Christophe Dutang

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

#####
# (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)