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

Laurent Gardes (1)

1 IRMA - Institut de Recherche Mathématique Avancée

The tail behavior of a survival function is controlled by the extreme value index. The aim of this paper is to propose a general procedure for the estimation of this parameter in the case where the observations are not necessarily distributed from the same distribution. 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. This procedure 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. A simulation study and a concrete application on financial data are proposed to illustrate the finite sample behavior of the proposed procedure.

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

Domaines: Statistiques [math.ST]

Laurent Gardes. A general estimator for the extreme value index: applications to conditional and heteroscedastic extremes. Extremes, 2015, 18 (3), pp.479--510. ⟨10.1007/s10687-015-0220-6⟩. ⟨hal-01075824v3⟩