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Title: A nonparametric estimator of the extremal index Authors:  Juan Juan Cai - Delft University of Technology (Netherlands) [presenting]
Andrea Krajina - Rabobank (Netherlands)
Abstract: The extremal index is a number in the unit interval determining the amount of tail dependence in a sequence of stationary random variables. It connects the standard extreme value theory of an iid sample to the case where the independence assumption no longer holds. It describes the clustering behavior of exceedances of a high threshold. We show that the extremal index is determined by the stable tail dependence function. We illustrate this link on theoretical examples and develop a nonparametric estimator of the extremal index. We prove that the estimator is consistent and asymptotically normal under some mixing conditions. The simulation study shows that the estimator has good finite sample properties and with the real-data example we provide an interesting application.