A general estimator for the right endpoint - with an application to supercentenarian women's records

TL;DR

This paper introduces a new, general estimator for the finite right endpoint of light-tailed distributions, applicable without estimating the extreme value index, supported by simulations and an application to supercentenarian women data.

Contribution

It extends existing endpoint estimators to a broader class of distributions and develops a new testing procedure for domain of attraction, enhancing practical endpoint estimation.

Findings

Estimator performs well when the extreme value index is above -1/2.

Simulation results show the estimator complements existing methods.

Application to supercentenarian data demonstrates practical utility.

Abstract

We extend the setting of the right endpoint estimator introduced in Fraga Alves and Neves (Statist. Sinica 24:1811--1835, 2014) to the broader class of light-tailed distributions with finite endpoint, belonging to some domain of attraction induced by the extreme value theorem. This stretch enables a general estimator for the finite endpoint, which does not require estimation of the (supposedly non-positive) extreme value index. A new testing procedure for selecting max-domains of attraction also arises in connection with asymptotic properties of the general endpoint estimator. The simulation study conveys that the general endpoint estimator is a valuable complement to the most usual endpoint estimators, particularly when the true extreme value index stays above $-1/2$, embracing the most common cases in practical applications. An illustration is provided via an extreme value analysis of supercentenarian women data.