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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DOI: 10.1016/S1631-073X(02)02486-X
Delafosse, Emmanuel 1; Guillou, Armelle 1

1 Université Paris VI, L.S.T.A., boı̂te 158, 4, place Jussieu, 75252 Paris cedex 05, France
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Delafosse, Emmanuel; Guillou, Armelle. 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. http://www.numdam.org/articles/10.1016/S1631-073X(02)02486-X/

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