Weighted estimation of the dependence function for an extreme-value distribution

TL;DR

This paper introduces a class of weighted estimators for the Pickands dependence function in bivariate extreme-value distributions, along with a jackknife empirical likelihood method for confidence intervals, validated through simulations.

Contribution

It proposes a new class of weighted estimators for the dependence function and a jackknife empirical likelihood approach for confidence intervals, improving over existing methods.

Findings

The proposed estimators perform well in simulations.

The jackknife empirical likelihood method effectively constructs confidence intervals.

The approach avoids complex variance estimation.

Abstract

Bivariate extreme-value distributions have been used in modeling extremes in environmental sciences and risk management. An important issue is estimating the dependence function, such as the Pickands dependence function. Some estimators for the Pickands dependence function have been studied by assuming that the marginals are known. Recently, Genest and Segers [Ann. Statist. 37 (2009) 2990-3022] derived the asymptotic distributions of those proposed estimators with marginal distributions replaced by the empirical distributions. In this article, we propose a class of weighted estimators including those of Genest and Segers (2009) as special cases. We propose a jackknife empirical likelihood method for constructing confidence intervals for the Pickands dependence function, which avoids estimating the complicated asymptotic variance. A simulation study demonstrates the effectiveness of our proposed jackknife empirical likelihood method.