Estimating the spectral measure of an extreme value distribution |
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Authors: | John HJ Einmahl Laurens de Haan Ashoke Kumar Sinha |
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Institution: | aDepartment of Mathematics and Computing Science, Eindhoven University of Technology, P.O. Box 513, 5600MB, Eindhoven, The Netherlands;bErasmus University, Rotterdam, The Netherlands |
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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. |
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Keywords: | Dependence structure Empirical process Estimation Functional central limit theorem Multivariate extremes Vapnik-Cervonenkis (VC) class |
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