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Etude de l'erreur relative d'approximation des quantiles extrêmes

Clément Albert 1 Anne Dutfoy 2 Stéphane Girard 1
1 MISTIS - Modelling and Inference of Complex and Structured Stochastic Systems
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, INPG - Institut National Polytechnique de Grenoble
Abstract : In the risk management context, the extreme value methodology consists in estimating extreme quantiles - one hundred years return period or more - from an extreme-value distribution adjusted on data. In this communication, we quantify the extrapolation limits associated with extreme quantile estimations. To this end, we focus on the framework of the block maxima method and we study the behaviour of the relative approximation error of a quantile estimate dedicated to the Gumbel attraction domain. We give necessary and sufficient conditions for the error to converge towards zero and, if necessary, we provide a first order approximation of the latter. We show that extrapolations can be greatly limited depending on the data distribution.
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https://hal.archives-ouvertes.fr/hal-01533220
Contributor : Stephane Girard <>
Submitted on : Tuesday, June 6, 2017 - 10:54:15 AM
Last modification on : Thursday, March 26, 2020 - 8:49:32 PM
Document(s) archivé(s) le : Thursday, September 7, 2017 - 12:48:31 PM

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Clément Albert, Anne Dutfoy, Stéphane Girard. Etude de l'erreur relative d'approximation des quantiles extrêmes. 49èmes Journées de Statistique organisées par la Société Française de Statistique, May 2017, Avignon, France. ⟨hal-01533220⟩

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