Comptes Rendus
Almost sure convergence of a tail index estimator in the presence of censoring
Comptes Rendus. Mathématique, Volume 335 (2002) no. 4, pp. 375-380.

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 Nr, the number of non-censored observations.

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 Nr de données non censurées.

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Revised:
Published online:
DOI: 10.1016/S1631-073X(02)02486-X

Emmanuel Delafosse 1; Armelle Guillou 1

1 Université Paris VI, L.S.T.A., boı̂te 158, 4, place Jussieu, 75252 Paris cedex 05, France
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Emmanuel Delafosse; Armelle Guillou. Almost sure convergence of a tail index estimator in the presence of censoring. Comptes Rendus. Mathématique, Volume 335 (2002) no. 4, pp. 375-380. doi : 10.1016/S1631-073X(02)02486-X. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(02)02486-X/

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[4] P. Deheuvels; E. Haeusler; D.M. Mason Almost sure convergence of the Hill estimator, Math. Proc. Cambridge Philos. Soc., Volume 104 (1988), pp. 371-381

[5] B.M. Hill A simple general approach to inference about the tail of a distribution, Ann. Statist., Volume 3 (1975), pp. 1163-1174

[6] G. Matthys, E. Delafosse, A. Guillou, J. Beirlant, Estimating high quantiles, Technical Report, 2002

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[8] I. Weissman Estimation of parameters and large quantiles based on the k largest observations, J. Amer. Statist. Assoc., Volume 73 (1978), pp. 812-815

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