Extreme quantiles estimation for actuarial applications

Emmanuel Delafosse; Armelle Guillou

doi:10.1016/j.crma.2004.06.005

Statistics/Probability Theory

Extreme quantiles estimation for actuarial applications

Presented by: Paul Deheuvels

Emmanuel Delafosse ¹; Armelle Guillou ¹

¹ Université Paris VI, L.S.T.A., boîte 158, 175, rue du Chevaleret, 75013 Paris, France

Comptes Rendus. Mathématique, Volume 339 (2004) no. 4, pp. 287-292.

Abstract
Résumé

This paper is devoted to the estimation of tail index and extreme quantiles in actuarial applications. In this domain, the observations are often censored. Nevertheless, conversely to the classical randomly right-censored model, the censoring variables are always observed. Therefore, under this assumption, we introduce new estimators and we study their asymptotic properties. Their behaviour are illustrated in a small simulation study.

Ce papier concerne l'estimation des indices de queues et des quantiles extrêmes dans des applications actuarielles. Dans ce domaine, les observations sont souvent censurées. Néanmoins, contrairement au modèle classique de censure aléatoire à droite, les données censurantes sont toujours observées. Sous cette condition, nous introduisons de nouveaux estimateurs et nous étudions leurs propriétés asymptotiques. Leur comportement est illustré sur la base de simulations.

Received: 2004-03-11
Accepted: 2004-06-07
Published online: 2004-07-23

DOI: 10.1016/j.crma.2004.06.005

Author's affiliations:

Emmanuel Delafosse ¹; Armelle Guillou ¹

¹ Université Paris VI, L.S.T.A., boîte 158, 175, rue du Chevaleret, 75013 Paris, France

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     title = {Extreme quantiles estimation for actuarial applications},
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     pages = {287--292},
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     doi = {10.1016/j.crma.2004.06.005},
     language = {en},
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Emmanuel Delafosse; Armelle Guillou. Extreme quantiles estimation for actuarial applications. Comptes Rendus. Mathématique, Volume 339 (2004) no. 4, pp. 287-292. doi : 10.1016/j.crma.2004.06.005. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2004.06.005/

References
Cited by

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

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