Weighted approximations of the tail empirical expectile process

Abstract : Expectiles define a least squares analogue of quantiles. They are determined by tail expectations rather than tail probabilities. For this reason and many other theoretical and practical merits, expec-tiles have recently received a lot of attention, especially in actuarial and financial risk management. Their estimation, however, typically requires to consider non-explicit asymmetric least squares estimates rather than the traditional order statistics used for quantile estimation. This makes the study of the tail expectile process a lot harder than that of the standard tail quantile process. Under the challenging model of heavy-tailed distributions, we derive joint weighted Gaus-sian approximations of the tail empirical expectile and quantile processes. We then use this powerful result to introduce and study new estimators of the tail index and extreme expectiles, as well as a novel expectile-based form of expected shortfall. Our estimators are built on general weighted combinations of both top order statistics and asymmetric least squares estimates. Some numerical simulations and an application to real data are provided.
Type de document :
Pré-publication, Document de travail
pp.1-30. 2018
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https://hal.archives-ouvertes.fr/hal-01744505
Contributeur : Stephane Girard <>
Soumis le : mardi 27 mars 2018 - 14:25:30
Dernière modification le : mercredi 11 avril 2018 - 01:58:11

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  • HAL Id : hal-01744505, version 1

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Abdelaati Daouia, Stephane Girard, Gilles Stupfler. Weighted approximations of the tail empirical expectile process. pp.1-30. 2018. 〈hal-01744505〉

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