Robust Estimation of Bivariate Tail Dependence Coefficient

TL;DR

This paper introduces robust estimators for the bivariate tail dependence coefficient that are less sensitive to outliers by using density power divergence, combining robust statistics with extreme value theory.

Contribution

It proposes novel robust estimators for tail dependence, analyzing their robustness and demonstrating their effectiveness through empirical studies on various distributions.

Findings

Proposed estimators exhibit high robustness to outliers.

Empirical results show improved estimation accuracy over traditional methods.

Influence function analysis confirms the robustness properties.

Abstract

The problem of estimating the coefficient of bivariate tail dependence is considered here from the robustness point of view; it combines two apparently contradictory theories of robust statistics and extreme value statistics. The usual maximum likelihood based or the moment type estimators of tail dependence coefficient are highly sensitive to the presence of outlying observations in data. This paper proposes some alternative robust estimators obtained by minimizing the density power divergence with suitable model assumptions; their robustness properties are examined through the classical influence function analysis. The performance of the proposed estimators is illustrated through an extensive empirical study considering several important bivariate extreme value distributions.