A0711
Title: A refined extreme quantiles estimator for Weibull tail-distributions
Authors: Jonathan El Methni - Universite Paris Cite (France) [presenting]
Stephane Girard - Inria (France)
Abstract: The problem of extreme quantiles estimation is addressed for Weibull tail distributions. Since such quantiles are asymptotically larger than the sample maxima, their estimation requires extrapolation methods. In the case of Weibull tail distributions, classical extreme-value estimators are numerically outperformed by estimators dedicated to this set of light-tailed distributions. The latter estimators of extreme quantiles are based on two estimators: an order statistic to estimate an intermediate quantile and an estimator of the Weibull tail coefficient. The common practice is to select the same intermediate sequence for both estimators. The aim is to show how an adapted choice of two different intermediate sequences leads to a reduction of the asymptotic bias associated with the resulting refined estimator. The asymptotic normality of the refined estimator is established, and a data-driven method is introduced for the practical selection of the intermediate sequences. The approach is compared to three estimators of extreme quantiles dedicated to Weibull tail distributions in a simulation study. An illustration of real data is also provided.