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On the relative approximation error of extreme quantiles by the block maxima method
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.
https://hal.archives-ouvertes.fr/hal-01571047
Contributor : Stephane Girard Connect in order to contact the contributor
Submitted on : Tuesday, August 1, 2017 - 2:45:19 PM
Last modification on : Friday, February 4, 2022 - 3:30:29 AM
Contributor : Stephane Girard Connect in order to contact the contributor
Submitted on : Tuesday, August 1, 2017 - 2:45:19 PM
Last modification on : Friday, February 4, 2022 - 3:30:29 AM
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