Comptes Rendus
Statistics/Probability Theory
Extreme quantiles estimation for actuarial applications
Comptes Rendus. Mathématique, Volume 339 (2004) no. 4, pp. 287-292.

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:
Accepted:
Published online:
DOI: 10.1016/j.crma.2004.06.005
Emmanuel Delafosse 1; Armelle Guillou 1

1 Université Paris VI, L.S.T.A., boîte 158, 175, rue du Chevaleret, 75013 Paris, France
@article{CRMATH_2004__339_4_287_0,
     author = {Emmanuel Delafosse and Armelle Guillou},
     title = {Extreme quantiles estimation for actuarial applications},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {287--292},
     publisher = {Elsevier},
     volume = {339},
     number = {4},
     year = {2004},
     doi = {10.1016/j.crma.2004.06.005},
     language = {en},
}
TY  - JOUR
AU  - Emmanuel Delafosse
AU  - Armelle Guillou
TI  - Extreme quantiles estimation for actuarial applications
JO  - Comptes Rendus. Mathématique
PY  - 2004
SP  - 287
EP  - 292
VL  - 339
IS  - 4
PB  - Elsevier
DO  - 10.1016/j.crma.2004.06.005
LA  - en
ID  - CRMATH_2004__339_4_287_0
ER  - 
%0 Journal Article
%A Emmanuel Delafosse
%A Armelle Guillou
%T Extreme quantiles estimation for actuarial applications
%J Comptes Rendus. Mathématique
%D 2004
%P 287-292
%V 339
%N 4
%I Elsevier
%R 10.1016/j.crma.2004.06.005
%G en
%F CRMATH_2004__339_4_287_0
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/

[1] A. Balkema; L. de Haan Residual life time at great age, Ann. Probab., Volume 2 (1974), pp. 792-804

[2] A.C. Davison; R.L. Smith Models for exceedances over high thresholds, J. Roy. Statist. Soc. Ser. B, Volume 52 (1990), pp. 393-442

[3] P. Hall On some simple estimates of an exponent of regular variation, J. Roy. Statist. Soc. Ser. B, Volume 44 (1982), pp. 37-42

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

[5] J. Pickands Statistical inference using extreme order statistics, Ann. Statist., Volume 3 (1975), pp. 119-131

[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

Cited by Sources:

Comments - Policy


Articles of potential interest

Almost sure convergence of a tail index estimator in the presence of censoring

Emmanuel Delafosse; Armelle Guillou

C. R. Math (2002)


A new extreme quantile estimator for heavy-tailed distributions

Amélie Fils; Armelle Guillou

C. R. Math (2004)


Asymptotic normality of the extreme quantile estimator based on the POT method

Jean Diebolt; Armelle Guillou; Pierre Ribereau

C. R. Math (2005)