Estimation of the extreme value index for non necessarily identically distributed observations

Laurent Gardes (1)

1 IRMA - Institut de Recherche Mathématique Avancée

It is well known that the tail behavior of a survival function S 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 independent but not necessarily distributed from the same distribution S. The proposed estimator only depends on a nonparametric estimator of the survival function S and can be applied to many different situations such as conditional extremes and heteroscedastic extremes. Its consistency is established under general conditions and its finite sample behavior is investigated through a simulation study.

Mots clés: Extreme value index; non-identically distributed observations; conditional extremes; heteroscedastic extremes

Domaines: Statistiques [math.ST]

Laurent Gardes. Estimation of the extreme value index for non necessarily identically distributed observations. 2014. ⟨hal-01075824v1⟩