A general estimator for the extreme value index: applications to conditional and heteroscedastic extremes

Laurent Gardes (1)

1 IRMA - Institut de Recherche Mathématique Avancée

It is well known that the tail behavior of a survival function is controlled by the so-called extreme value index. The aim of this paper is the estimation of this extreme value index in the case where the observations are not necessarily distributed from the same distribution. A general procedure of estimation is proposed. The idea is to estimate in a consistent way the survival function and to apply a general functional to obtain a consistent estimator for the extreme value index. The procedure of estimation presented in this paper permits to deal with a large set of models such as conditional extremes and heteroscedastic extremes. The consistency of the obtained estimator is established under general conditions and its finite sample behavior is investigated through a simulation study.

Mots clés: Extreme value index; conditional extremes; heteroscedastic extremes; Consistency

Domaines: Statistiques [math.ST]

Laurent Gardes. A general estimator for the extreme value index: applications to conditional and heteroscedastic extremes. 2015. ⟨hal-01075824v2⟩