RTDEfit function

Fitting a Tail Dependence model with a Robust Estimator

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, ...)

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 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") .

Returns

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.

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).

Author(s)

Christophe Dutang

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)