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
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.
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Submitted on : Tuesday, August 1, 2017 - 2:45:19 PM
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Clément Albert, Anne Dutfoy, Stéphane Girard. On the relative approximation error of extreme quantiles by the block maxima method. 10th International Conference on Extreme Value Analysis, Jun 2017, Delft, Netherlands. 10th International Conference on Extreme Value Analysis, 2017. 〈hal-01571047〉

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