Robust and Smooth Estimation of the Extreme Tail Index via Weighted Minimum Density Power Divergence

TL;DR

This paper proposes a new class of robust, smooth estimators for the tail index of Pareto-type distributions using weighted density power divergence, improving outlier robustness and efficiency.

Contribution

It introduces a weighted density power divergence-based estimator, generalizing existing methods with proven consistency and asymptotic normality.

Findings

Enhanced robustness to outliers.

Improved finite-sample performance in simulations.

Generalizes weighted least squares and kernel estimators.

Abstract

By introducing a weight function into the density power divergence, we develop a new class of robust and smooth estimators for the tail index of Pareto-type distributions, offering improved efficiency in the presence of outliers. These estimators can be viewed as a robust generalization of both weighted least squares and kernel-based tail index estimators. We establish the consistency and asymptotic normality of the proposed class. A simulation study is conducted to assess their finite-sample performance in comparison with existing methods.