Comptes Rendus
Statistics
Asymptotic normality of the extreme quantile estimator based on the POT method
Comptes Rendus. Mathématique, Volume 341 (2005) no. 5, pp. 307-312.

The POT (Peaks-Over-Threshold) approach consists in using the generalized Pareto distribution (GPD) to approximate the distribution of excesses over thresholds. In this Note, we propose extreme quantile estimators based on this method. We establish their asymptotic normality under suitable general assumptions.

La méthode POT (pics au-delà d'un seuil) consiste à utiliser une distribution de Pareto généralisée (GPD) pour approximer la loi des excès au-delà d'un seuil. Dans cette Note, nous proposons des estimateurs de quantiles extrêmes basés sur cette méthode. Nous établissons leurs normalités asymptotiques sous des hypothèses générales.

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DOI: 10.1016/j.crma.2005.06.032
Jean Diebolt 1; Armelle Guillou 2; Pierre Ribereau 2

1 CNRS, université de Marne-la-Vallée, équipe d'analyse et de mathématiques appliquées, 5, boulevard Descartes, bâtiment Copernic, Champs-sur-Marne, 77454 Marne-la-Vallée cedex 2, France
2 Université Paris VI, laboratoire de statistique théorique et appliquée, boîte 158, 175, rue du Chevaleret, 75013 Paris, France
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Jean Diebolt; Armelle Guillou; Pierre Ribereau. Asymptotic normality of the extreme quantile estimator based on the POT method. Comptes Rendus. Mathématique, Volume 341 (2005) no. 5, pp. 307-312. doi : 10.1016/j.crma.2005.06.032. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2005.06.032/

[1] L. de Haan; H. Rootzén On the estimation of high quantiles, J. Statist. Plann. Inference, Volume 35 (1993), pp. 1-13

[2] L. de Haan; U. Stadtmüller Generalized regular variation of second order, J. Austral. Math. Soc. Ser. A, Volume 61 (1996), pp. 381-395

[3] J. Diebolt, A. Guillou, P. Ribereau, Asymptotic normality of extreme quantile estimators based on the peaks-over-threshold approach, submitted for publication, 2005

[4] H. Drees On smooth statistical tail functionals, Scand. J. Statist., Volume 25 (1998) no. 1, pp. 187-210

[5] H. Drees; A. Ferreira; L. de Haan On maximum likelihood estimation of the extreme value index, Ann. Appl. Probab., Volume 14 (2004) no. 3, pp. 1179-1201

[6] B.V. Gnedenko Sur la distribution limite du terme maximum d'une série aléatoire, Ann. Math., Volume 44 (1943), pp. 423-453

[7] J. Pickands Statistical inference using extreme order statistics, Ann. Statist., Volume 3 (1975), pp. 119-131

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