Estimating the mean of a heavy-tailed distribution under random censoring

TL;DR

This paper proposes an alternative method for estimating the mean of heavy-tailed distributions under random censoring, ensuring asymptotic normality where traditional CLT-based methods fail, validated through simulation studies.

Contribution

It introduces a novel estimation approach leveraging extreme value theory to handle heavy tails under censoring, ensuring asymptotic normality.

Findings

The new estimator performs well in simulations.

It extends mean estimation to heavy-tailed censored data.

Traditional CLT-based methods may not hold for such distributions.

Abstract

The central limit theorem introduced by Stute [The central limit theorem under random censorship. Ann. Statist. 1995; 23: 422-439] does not hold for some class of heavy-tailed distributions. In this paper, we make use of the extreme value theory to propose an alternative estimating approach of the mean ensuring the asymptotic normality property. A simulation study is carried out to evaluate the performance of this estimation procedure