Nonparametric estimator of the tail dependence coefficient: balancing bias and variance

TL;DR

This paper introduces a new method for optimally selecting the threshold in a nonparametric tail dependence estimator, balancing bias and variance, and demonstrates its effectiveness through simulations.

Contribution

A novel semiparametric threshold selection method that improves the accuracy of tail dependence estimation by combining theoretical MSE with copula estimation.

Findings

The proposed method outperforms existing approaches in simulations.

It effectively balances bias and variance in tail dependence estimation.

The method integrates theoretical and parametric insights for better threshold choice.

Abstract

A theoretical expression is derived for the mean squared error of a nonparametric estimator of the tail dependence coefficient, depending on a threshold that defines which rank delimits the tails of a distribution. We propose a new method to optimally select this threshold. It combines the theoretical mean squared error of the estimator with a parametric estimation of the copula linking observations in the tails. Using simulations, we compare this semiparametric method with other approaches proposed in the literature, including the plateau-finding algorithm.