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Journal Articles Extremes Year : 2023

A refined Weissman estimator for extreme quantiles

Abstract

Weissman extrapolation methodology for estimating extreme quantiles from heavy-tailed distributions is based on two estimators: an order statistic to estimate an intermediate quantile and an estimator of the tail-index. The common practice is to select the same intermediate sequence for both estimators. In this work, we show how an adapted choice of two different intermediate sequences leads to a reduction of the asymptotic bias associated with the resulting refined Weissman 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 Weissman estimator and to six bias reduced estimators of extreme quantiles on a large scale simulation study. It appears that the refined Weissman estimator outperforms its competitors in a wide variety of situations, especially in the challenging high bias cases. Finally, an illustration on an actuarial real data set is provided.
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Dates and versions

hal-03266676 , version 1 (22-06-2021)
hal-03266676 , version 2 (08-09-2021)
hal-03266676 , version 3 (15-03-2022)

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Michaël Allouche, Jonathan El Methni, Stéphane Girard. A refined Weissman estimator for extreme quantiles. Extremes, 2023, 26, pp.545-572. ⟨10.1007/s10687-022-00452-8⟩. ⟨hal-03266676v3⟩
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