A Lynden-Bell integral estimator for extremes of randomly truncated data

TL;DR

This paper introduces a Lynden-Bell integral estimator for accurately estimating extreme value indices and quantiles in heavy-tailed data subject to random right truncation, with proven asymptotic normality.

Contribution

It proposes a novel estimator based on Lynden-Bell integrals for extremes in truncated heavy-tailed data, extending existing methods.

Findings

Estimator demonstrates asymptotic normality under mild conditions.

Simulation results show high accuracy across various scenarios.

Method outperforms traditional estimators in truncated data settings.

Abstract

This work deals with the estimation of the extreme value index and extreme quantiles for heavy tailed data,randomly right truncated by another heavy tailed variable. Under mild assumptions and the condition thatthe truncated variable is less heavy-tailed than the truncating variable, asymptotic normality is proved for bothestimators. The proposed estimator of the extreme value index is an adaptation of the Hill estimator, in thenatural form of a Lynden-Bell integral. Simulations illustrate the quality of the estimators under a variety ofsituations.