Moment estimators of the extreme value index for randomly censored data in the Weibull domain of attraction

TL;DR

This paper develops new moment-based estimators for the extreme value index in Weibull domain of attraction under random censoring, adapting previous heavy-tailed methods to the negative index case, with proven consistency and simulation validation.

Contribution

It introduces two families of weighted moment estimators for the negative extreme value index under censoring, extending existing methods to a new domain and proving their consistency.

Findings

Estimators are consistent under first order conditions.

Simulation results demonstrate good performance of the estimators.

Method adapts heavy-tailed approaches to Weibull domain.

Abstract

This paper addresses the problem of estimating the extreme value index in presence of random censoring for distributions in the Weibull domain of attraction. The methodologies introduced in [Worms (2014)], in the heavy-tailed case, are adapted here to the negative extreme value index framework, leading to the definition of weighted versions of the popular moments of relative excesses with arbitrary exponent. This leads to the definition of two families of estimators (with an adaptation of the so called Moment estimator as a particular case), for which the consistency is proved under a first order condition. Illustration of their performance, issued from an extensive simulation study, are provided.