High-dimensional variables clustering based on sub-asymptotic maxima of a weakly dependent random process

Description

The dependence structure between extreme observations can be complex. For that purpose, we see clustering as a tool for learning the complexextremal 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 identifiableallowing statistical inference. With a dedicated algorithm, we show that sample versions of the extremal correlation can be used to recover theclusters of variables without specifying the number of clusters. Our algorithm has a computational complexity that is polynomial in the dimensionand it is shown to be strongly consistent in growing dimensions where observations are drawn from a stationary mixing process. This implies thatgroups 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.

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