Asymptotic behavior of the extrapolation error associated with the estimation of extreme quantiles

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 : We investigate the asymptotic behavior of the (relative) extrapolation error associated with some estimators of extreme quantiles based on extreme-value theory. It is shown that the extrapolation error can be interpreted as the remainder of a first order Taylor expansion. Necessary and sufficient conditions are then provided such that this error tends to zero as the sample size increases. Interestingly, in case of the so-called Exponential Tail estimator, these conditions lead to a subdivision of Gumbel maximum domain of attraction into three subsets. In constrast, the extrapolation error associated with Weissman estimator has a common behavior over the whole Fréchet maximum domain of attraction. First order equivalents of the extrapolation error are then derived and their accuracy is illustrated numerically.
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Pré-publication, Document de travail
2018
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Soumis le : lundi 26 février 2018 - 14:05:02
Dernière modification le : mercredi 11 avril 2018 - 01:58:12

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Clément Albert, Anne Dutfoy, Stéphane Girard. Asymptotic behavior of the extrapolation error associated with the estimation of extreme quantiles. 2018. 〈hal-01692544v2〉

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