Tail product-limit process for truncated data with application to extreme value index estimation

TL;DR

This paper introduces a new estimator for the extreme value index based on a tail product-limit process, specifically designed for Pareto-like distributions with right truncation, supported by theoretical and simulation results.

Contribution

It develops a weighted Gaussian approximation for the tail product-limit process and proposes a new consistent, asymptotically normal estimator for the extreme value index under right truncation.

Findings

Estimator shows good finite sample performance in simulations

Theoretical properties include consistency and asymptotic normality

Applicable to Pareto-like distributions with right truncation

Abstract

A weighted Gaussian approximation to tail product-limit process for Pareto-like distributions of randomly right-truncated data is provided and a new consistent and asymptotically normal estimator of the extreme value index is derived. A simulation study is carried out to evaluate the finite sample behavior of the proposed estimator.