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Comptes Rendus Mathématique
Volume 335, n° 4
pages 375-380 (2002)
Doi : S1631-073X(02)02486-X
Received : 8 April 2002 ; 
Almost sure convergence of a tail index estimator in the presence of censoring
Convergence presque sûre d'un index de queue en présence de censure
 

Emmanuel Delafosse , Armelle Guillou
Université Paris VI, L.S.T.A., boı̂te 158, 4, place Jussieu, 75252 Paris cedex 05, France 

Note presented by Paul Deheuvels

Abstract

In Beirlant and Guillou [1] an exponential regression model was introduced on the basis of scaled log-spacing between subsequent extreme order statistics from a Pareto-type distribution in the presence of censoring. From this representation, they derived an estimator for the Pareto index. In this note, we revisit this adaptation of the popular Hill [5] estimator for heavy-tailed distributions, generalizing the almost sure convergence of this estimator under very general conditions on N r , the number of non-censored observations. To cite this article: E. Delafosse, A. Guillou, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 375-380.

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

Dans Beirlant et Guillou [1] un modèle de régression exponentiel basé sur l'écart du logarithme de statistiques d'ordres consécutives d'un échantillon issu d'une loi de type Pareto a été introduit en présence de censure. De cette représentation, ils obtiennent un estimateur de l'index de Pareto. Dans cette note, nous revisitons cette adaptation de l'estimateur de Hill [5] en établissant en particulier sa convergence presque sûre sous des conditions très générales sur le nombre N r de données non censurées. Pour citer cet article : E. Delafosse, A. Guillou, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 375-380.

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


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