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

International audience; 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.