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

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Abstract

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.

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Authors and Affiliations

  1. Université de Strasbourg & CNRS, IRMA, UMR 7501, 7 rue René Descartes, 67084, Strasbourg Cedex, France

    Laurent Gardes

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  1. Laurent Gardes
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Correspondence to Laurent Gardes.

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Gardes, L. A general estimator for the extreme value index: applications to conditional and heteroscedastic extremes. Extremes 18, 479–510 (2015). https://doi.org/10.1007/s10687-015-0220-6

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  • DOI: https://doi.org/10.1007/s10687-015-0220-6

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