Nelson-Aalen tail product-limit process and extreme value index estimation under random censorship

TL;DR

This paper introduces a new estimator for the extreme value index in heavy-tailed, right-censored data, based on Nelson-Aalen's estimator, with proven asymptotic properties and improved performance demonstrated through simulations.

Contribution

It proposes a novel, consistent reduced-bias estimator for the extreme value index under random censorship, with theoretical asymptotic normality.

Findings

The new estimator outperforms existing methods in simulations.

Asymptotic normality is established under second-order regular variation.

Provides a weak approximation to the tail product-limit process for censored data.

Abstract

On the basis of Nelson-Aalen nonparametric estimator of the cumulative distribution function, we provide a weak approximation to tail product-limit process for randomly right-censored heavy-tailed data. In this context, a new consistent reduced-bias estimator of the extreme value index is introduced and its asymptotic normality is established only by assuming the second-order regular variation of the underlying distribution function. A simulation study shows that the newly proposed estimator performs better than the existing ones.