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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Emmanuel Delafosse 1; Armelle Guillou 1
@article{CRMATH_2002__335_4_375_0, author = {Emmanuel Delafosse and Armelle Guillou}, title = {Almost sure convergence of a tail index estimator in the presence of censoring}, journal = {Comptes Rendus. Math\'ematique}, pages = {375--380}, publisher = {Elsevier}, volume = {335}, number = {4}, year = {2002}, doi = {10.1016/S1631-073X(02)02486-X}, language = {en}, }
TY - JOUR AU - Emmanuel Delafosse AU - Armelle Guillou TI - Almost sure convergence of a tail index estimator in the presence of censoring JO - Comptes Rendus. Mathématique PY - 2002 SP - 375 EP - 380 VL - 335 IS - 4 PB - Elsevier DO - 10.1016/S1631-073X(02)02486-X LA - en ID - CRMATH_2002__335_4_375_0 ER -
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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