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Conference Papers Year : 2022

A refined Weissman estimator for extreme quantiles


Weissman's 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. 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 in a large-scale simulation study. It appears that the refined Weissman estimator outperforms its competitors in a wide variety of situations, especially in challenging high-bias cases. Finally, an illustration of an actuarial real data set is provided.
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Dates and versions

hal-03764409 , version 1 (30-08-2022)


  • HAL Id : hal-03764409 , version 1


Michaël Allouche, Jonathan El Methni, Stéphane Girard. A refined Weissman estimator for extreme quantiles. Compstat 2022 - 24th International Conference on Computational Statistics, Aug 2022, Bologna, Italy. ⟨hal-03764409⟩
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