Title: Feature clustering and tests for asymptotic independence
Authors: Anne Sabourin - Telecom Paris, Institut Polytechnique de Paris (France) [presenting]
Mael Chiapino - Telecom ParisTech (France)
Johan Segers - Universite catholique de Louvain (Belgium)
Abstract: Sparsity in multivariate extremes may be defined as the concentration of the angular measure on low dimensional subsets of the unit sphere. In a high dimensional context ($d>50$), a natural first step when analyzing the dependence structure of extreme event is to identify such a pattern. Earlier works have proposed different algorithms for this purpose. The stopping criterion for the CLEF algorithm is shown to be a linear combination of extremal coefficients. This allows us to interpret the CLEF algorithm, up to a minor re-tuning of its stopping criterion, as a sequence of tests for multivariate asymptotic full dependence between various subsets of components, with asymptotic guarantees. We also propose deeper modifications of the CLEF algorithm obtained by replacing the null hypothesis of asymptotic dependence with that of asymptotic independence and using test statistics based on coefficients of multivariate tail dependence.