Robust estimations for the tail index of Weibull-type distribution

TL;DR

This paper introduces robust M-estimators for the Weibull tail index that handle contaminated data effectively, providing asymptotic normality and demonstrated robustness through simulations and real data analysis.

Contribution

It proposes new flexible M-estimators for Weibull tail index with robustness features and asymptotic properties, addressing contamination issues in tail estimation.

Findings

Estimators are asymptotically normal with √n convergence.

Robustness is validated through influence function analysis.

Simulation and empirical study confirm effectiveness.

Abstract

Based on suitable left-truncated or censored data, two flexible classes of $M$-estimations of Weibull tail coefficient are proposed with two additional parameters bounding the impact of extreme contamination. Asymptotic normality with $\sqrt {n}$-rate of convergence is obtained. Its robustness is discussed via its asymptotic relative efficiency and influence function. It is further demonstrated by a small scale of simulations and an empirical study on CRIX.