Estimation of Tails and Related Quantities Using the Number of Near-Extremes

Détails

ID Serval
serval:BIB_2750626C5DD0
Type
Article: article d'un périodique ou d'un magazine.
Collection
Publications
Titre
Estimation of Tails and Related Quantities Using the Number of Near-Extremes
Périodique
Communications in Statistics - Theory and Methods
Auteur⸱e⸱s
Hashorva E., Hüsler J.
ISSN
0361-0926
Statut éditorial
Publié
Date de publication
2005
Peer-reviewed
Oui
Volume
34
Numéro
2
Pages
337-349
Langue
anglais
Résumé
In an insurance context, consider {X-n, n > 1} random claim sizes with common distribution function F and {N(t), t >= 0} an integer valued stochastic process that counts the number of claims occurring during the time interval [0, t]. Based on the number of near-extremes which are the observations X-1 near the largest or the mth largest observation, we derive in this article a strongly consistent estimator of upper tails of X-1. Furthermore, estimators for both the tail index and the upper endpoint are introduced when F is a generalized Pareto distribution. Asymptotic normal law for the proposed estimators is additionally presented.
Mots-clé
Asymptotic normality, Estimation of tail index, Estimation of the upper endpoint, Generalized Pareto distribution, Number of near-extremes
Web of science
Création de la notice
03/09/2010 12:00
Dernière modification de la notice
20/08/2019 14:06
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