angscdf {extremis}

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)

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.

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).

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.

Author(s)

Miguel de Carvalho

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)