A refined extreme quantiles estimator of Weibull tail-distributions

Jonathan El Methni (1) , Stéphane Girard (2)

1 MAP5 - UMR 8145 - Mathématiques Appliquées Paris 5
2 STATIFY - Modèles statistiques bayésiens et des valeurs extrêmes pour données structurées et de grande dimension

In the case of Weibull tail distributions, the most commonly used methodology for estimating extreme quantiles is 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. We 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 latter estimator is established, and a data-driven method is introduced for the practical selection of the intermediate sequences. Our approach is compared to various bias-reduced estimators in a simulation study.

Domaines: Statistiques [math.ST]

Jonathan El Methni, Stéphane Girard. A refined extreme quantiles estimator of Weibull tail-distributions. CMStatistics 2022 - 15th International Conference of the ERCIM WG on Computational and Methodological Statistics, Dec 2022, London, United Kingdom. ⟨hal-03910631⟩