Estimating POT Second-order Parameter for Bias Correction

TL;DR

This paper introduces a penalized estimator for the POT second-order parameter to reduce bias in estimating the stable tail dependence function, improving extremal dependence analysis.

Contribution

It proposes a novel penalized estimator for the second-order parameter, with proven asymptotic consistency and bias correction capabilities.

Findings

Estimator is asymptotically consistent

Bias in stable tail dependence estimation is reduced

Empirical results show improved extremal dependence estimation

Abstract

The stable tail dependence function provides a full characterization of the extremal dependence structures. Unfortunately, the estimation of the stable tail dependence function often suffers from significant bias, whose scale relates to the Peaks-Over-Threshold (POT) second-order parameter. For this second-order parameter, this paper introduces a penalized estimator that discourages it from being too close to zero. This paper then establishes this estimator's asymptotic consistency, uses it to correct the bias in the estimation of the stable tail dependence function, and illustrates its desirable empirical properties in the estimation of the extremal dependence structures.