Bias-reduced extreme quantiles estimators of Weibull-tail distributions

TL;DR

This paper introduces a new bias-reduced estimator for extreme quantiles of Weibull-tail distributions, based on an exponential regression model, with proven asymptotic normality and adaptive selection, validated through simulations and real data.

Contribution

It proposes a novel bias-reduced extreme quantile estimator for Weibull tails, improving accuracy over classical methods with an adaptive selection procedure.

Findings

Estimator has reduced bias compared to classical methods

Asymptotic normality of the estimator is established

Simulation and real data demonstrate efficiency

Abstract

In this paper, we consider the problem of estimating an extreme quantile of a Weibull tail-distribution. The new extreme quantile estimator has a reduced bias compared to the more classical ones proposed in the literature. It is based on an exponential regression model that was introduced in Diebolt et al. (2008). The asymptotic normality of the extreme quantile estimator is established. We also introduce an adaptive selection procedure to determine the number of upper order statistics to be used. A simulation study as well as an application to a real data set are provided in order to prove the efficiency of the above mentioned methods.