extremis (version 1.2.1)

angscdf: Smooth Empirical-Likelihood Based Inference for the Angular Measure

Description

This function computes smooth empirical-likelihood based estimators for the angular distribution function of a bivariate extreme value distribution.

Usage

angscdf(Y, tau = 0.95, nu, grid = seq(0.01, 0.99, length = 2^8),
	method = "euclidean", raw = TRUE)

Value

H

the estimated angular distribution function values.

grid

grid with coordinates of the points where the angular measure is estimated.

w

pseudo-angles.

nu

concentration parameter of the Beta-kernel.

Y

raw data.

The plot method depicts the empirical likelihood-based angular distribution function.

Arguments

Y

data frame with two columns from which the estimate is to be computed.

tau

value used to threshold the data; by default it is set as the 0.95 quantile of the pseudo-radius tau = 0.95.

nu

concentration parameter of beta distribution which controls the amount of smoothing.

grid

grid with coordinates of the points where the angular measure is estimated; by default grid = seq(0.01, 0.99, length = 2^8).

method

a character string setting the method to be used. By default method = "euclidean", the other option being method = "empirical". See details.

raw

logical; if TRUE, Y will be converted to unit Fréchet scale. If FALSE, Y will be understood as already in unit Fréchet scale.

Author

Miguel de Carvalho

Details

method = "euclidean" implements the maximum Euclidean likelihood spectral distribution function as introduced by de Carvalho et al (2013). method = "empirical" implements the maximum Empirical likelihood spectral distribution function as introduced by Einmahl and Segers (2009).

References

de Carvalho, M., Oumow, B., Segers, J. and Warchol, M. (2013) A Euclidean likelihood estimator for bivariate tail dependence. Communications in Statistics---Theory and Methods, 42, 1176--1192.

Einmahl, J. H. J., and Segers, J. (2009) Maximum empirical likelihood estimation of the spectral measure of an extreme-value distribution. The Annals of Statistics, 37, 2953--2989.

Examples

## de Carvalho et al (2013, Fig. 7)
data(beatenberg)
attach(beatenberg)
fit <- angscdf(beatenberg, tau = 0.98, nu = 163, raw = FALSE)
plot(fit)
rug(fit$w)