[Un estimateur de l'indice des valeurs extrêmes à double seuil]
Dans cette Note, nous proposons un estimateur de l'indice des valeurs extrêmes construit en utilisant uniquement le nombre de points qui dépassent des seuils aléatoires. On démontre qu'il est faiblement consistant et asymptotiquement normal. Du résultat de convergence en loi, on déduit que la vitesse de convergence de notre estimateur est une puissance de la taille de l'échantillon. A notre connaissance, cette vitesse n'est atteinte par aucun autre estimateur de l'indice des valeurs extrêmes. A l'aide de simulations, nous comparons notre estimateur à l'estimateur des moments (Dekkers et al., Ann. Statist. 17 (1989) 1833–1855).
The purpose of this Note is to propose an estimator of the extreme value index constructed by using only the number of points exceeding random thresholds. We prove the weak consistency and the asymptotic normality of this estimator. We deduce from this last result that the rate of convergence of our estimator is in a power of the sample size. To our knowledge, this rate of convergence is not reached by any other estimate of the extreme value index. Through a simulation, we compare our estimator to the moment estimator (Dekkers et al., Ann. Statist. 17 (1989) 1833–1855).
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@article{CRMATH_2003__337_4_287_0,
author = {Laurent Gardes},
title = {Double-thresholded estimator of extreme value index},
journal = {Comptes Rendus. Math\'ematique},
pages = {287--292},
publisher = {Elsevier},
volume = {337},
number = {4},
year = {2003},
doi = {10.1016/S1631-073X(03)00329-7},
language = {en},
}
Laurent Gardes. Double-thresholded estimator of extreme value index. Comptes Rendus. Mathématique, Volume 337 (2003) no. 4, pp. 287-292. doi : 10.1016/S1631-073X(03)00329-7. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(03)00329-7/
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