Statistics of extremes under random censoring

TL;DR

This paper studies how to estimate the extreme value index and extreme quantiles when data are randomly censored, providing asymptotic results, simulations, and medical data applications.

Contribution

It offers a unified theoretical framework for asymptotic normality of estimators under random censoring and demonstrates their practical effectiveness.

Findings

Asymptotic normality results for various estimators

Simulation studies showing estimator performance

Application to medical censored data

Abstract

We investigate the estimation of the extreme value index when the data are subject to random censorship. We prove, in a unified way, detailed asymptotic normality results for various estimators of the extreme value index and use these estimators as the main building block for estimators of extreme quantiles. We illustrate the quality of these methods by a small simulation study and apply the estimators to medical data.