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Comptes Rendus Mathématique
Volume 341, n° 1
pages 53-58 (juillet 2005)
Doi : 10.1016/j.crma.2005.05.023
Received : 18 January 2005 ;  accepted : 24 May 2005
Asymptotic distribution of a Pickands-type estimator of the extreme-value index
Loi asymptotique dʼun estimateur de type Pickands de lʼindice des valeurs extrêmes
 

Laurent Gardes a , Stéphane Girard b
a Université Grenoble 2, LABSAD, B.P. 47, 38040 Grenoble cedex 9, France 
b Université Grenoble 1, LMC-IMAG, B.P. 53, 38041 Grenoble cedex 9, France 

Abstract

One of the main goals of extreme-value analysis is to estimate the probability of rare events given a sample from an unknown distribution. The upper tail behavior of this distribution is described by the extreme-value index . The aim of this Note is to establish the asymptotic distribution of the estimator of   introduced in Gardes and Girard [A Pickands-type estimator of the extreme-value index, Technical Report LMC-IMAG, RR-1063, 2004]. We also give its rate of convergence in some typical situations. To cite this article: L. Gardes, S. Girard, C. R. Acad. Sci. Paris, Ser. I 341 (2005).

The full text of this article is available in PDF format.
Résumé

Dans de nombreuses applications, on sʼintéresse à lʼestimation de probabilités dʼévènements rares étant donné un échantillon dʼune loi inconnue. Pour ce faire, il est généralement indispensable dʼestimer au préalable lʼindice des valeurs extrêmes qui caractérise le type de décroissance de la queue de distribution. Lʼobjectif de cette Note est de déterminer la loi asymptotique de lʼestimateur de   défini dans Gardes et Girard [A Pickands-type estimator of the extreme-value index, Technical Report LMC-IMAG, RR-1063, 2004] et dʼen déduire sa vitesse de convergence pour certains modèles. Pour citer cet article : L. Gardes, S. Girard, C. R. Acad. Sci. Paris, Ser. I 341 (2005).

The full text of this article is available in PDF format.


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