Dependence of Multivariate Extremes
We give necessary and sufficient conditions for two sub-vectors of a random vector with a multivariate extreme value (MEV) distribution, corresponding to the limit distribution of the maximum of a multidimensional stationary sequence with extremal index, to be independent or totally dependent. Those conditions involve first relations between the multivariate extremal indices of the sequences and secondly a coefficient that measures the strength of dependence between both sub-vectors. The main results are illustrated with an auto-regressive sequence and a 3-dependent sequence.
The authors thank the referees for all the helpful remarks. This research was supported by the research unit “Centro de Matemática” of the University of Beira Interior through the Foundation for Science and Technology (FCT).
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