# RTDEfit: Fitting a Tail Dependence model with a Robust Estimator In RTDE: Robust Tail Dependence Estimation

## Description

Fit a Tail Dependence model with a Robust Estimator.

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10``` ```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 (η,τ are fitted while ρ is fixed) on the relative excess of Z_ω (see `zvalueRTDE`) using a robust estimator based on the minimum distance power divergence criterion (see `MDPD`). The boundary enforcement on η,τ 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 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16``` ```##### # (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) ```

RTDE documentation built on Jan. 8, 2020, 5:09 p.m.