On the relative approximation error of extreme quantiles by the block maxima method

Clément Albert; Anne Dutfoy; Stéphane Girard

On the relative approximation error of extreme quantiles by the block maxima method

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

2 EDF R&D MRI - Management des Risques Industriels

Abstract : This study takes place in the context of extreme quantiles estimation by the block maxima method. We investigate the behaviour of the relative approximation error of a quantile estimator dedicated to the Gumbel maximum domain of attraction. Our work is based on a regular variation assumption on the first derivative of the logarithm of the inverse cumulative hazard rate function, introduced by de Valk (2016) [Approximation of high quantiles from intermediate quantiles. Extremes 19(4), 661-686]. We give necessary and sufficient conditions under which the relative approximation error of the extreme quantile computed with the block maxima method converges to zero. We also provide a first order approximation of the relative approximation error when the latter converges towards zero. Our results are illustrated on simulated data.

Keywords : regular variation Extreme quantiles estimation relative approximation error asymptotic properties

Document type :

Conference papers

Domain :

Mathematics [math] / Statistics [math.ST]

Liste complète des métadonnées

https://hal.archives-ouvertes.fr/hal-01571047
Contributor : Stephane Girard <>
Submitted on : Tuesday, August 1, 2017 - 2:45:19 PM
Last modification on : Saturday, March 9, 2019 - 10:19:15 PM

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On the relative approximation error of extreme quantiles by the block maxima method

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