A Lynden-Bell integral estimator for the tail index of right-truncated data with a random threshold

TL;DR

This paper introduces a new Hill-type estimator for the tail index of right-truncated Pareto data using a Lynden-Bell integral with a random threshold, demonstrating its theoretical properties and finite sample performance.

Contribution

It extends previous work by deriving a Hill-type estimator with a random threshold, establishing its consistency and asymptotic normality.

Findings

Estimator is consistent and asymptotically normal.

Simulation shows good finite sample performance.

Improves tail index estimation for truncated data.

Abstract

By means of a Lynden-Bell integral with deterministic threshold, Worms and Worms [A Lynden-Bell integral estimator for extremes of randomly truncated data. Statist. Probab. Lett. 2016; 109: 106-117] recently introduced an asymptotically normal estimator of the tail index for randomly right-truncated Pareto-type data. In this context, we consider the random threshold case to derive a Hill-type estimator and establish its consistency and asymptotic normality. A simulation study is carried out to evaluate the finite sample behavior of the proposed estimator.