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Title: High-dimensional variables clustering based on sub-asymptotic maxima of a weakly dependent random process Authors:  Alexis Boulin - Universite Cote d'Azur and Inria, Lemon (France) [presenting]
Elena Di Bernardino - University Cote de Azur (France)
Thomas Laloe - LJAD - Universite de Nice (France)
Gwladys Toulemonde - Université de Montpellier (France)
Abstract: The dependence structure between extreme observations can be complex. For that purpose, we see clustering as a tool for learning the complex extremal dependence structure. We introduce the Asymptotic Independent block (AI-block) model, a model-based clustering where population-level clusters are clearly defined using independence of clusters' maxima of a multivariate random process. This class of models is identifiable allowing statistical inference. With a dedicated algorithm, we show that sample versions of the extremal correlation can be used to recover the clusters of variables without specifying the number of clusters. Our algorithm has a computational complexity that is polynomial in the dimension and it is shown to be strongly consistent in growing dimensions where observations are drawn from a stationary mixing process. This implies that groups can be learned in a completely nonparametric inference in the study of dependent processes where block maxima are only subasymptotic, i.e., approximately extreme value distributed.