Estimating the spectral measure of an extreme value distribution

J.H.J. Einmahl, L. Haan, de, A.K. Sinha

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    Abstract

    Let (X1, Y1), (X2, Y2),…, (Xn, Yn) be a random sample from a bivariate distribution function F which is in the domain of attraction of a bivariate extreme value distribution function G. This G is characterized by the extreme value indices and its spectral measure or angular measure. The extreme value indices determine both the marginals and the spectral measure determines the dependence structure. In this paper, we construct an empirical measure, based on the sample, which is a consistent estimator of the spectral measure. We also show for positive extreme value indices the asymptotic normality of the estimator under a suitable 2nd order strengthening of the bivariate domain of attraction condition.
    Original languageEnglish
    Pages (from-to)143-171
    JournalStochastic Processes and their Applications
    Volume70
    Issue number2
    DOIs
    Publication statusPublished - 1997

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