Séance Séminaire

Séminaire de Probabilités et Statistique

Multivariate Sparse Clustering for Extremes [ATTENTION : jeudi 15h]

Studying the tail dependence of multivariate extremes is a major challenge in extreme value analysis. Under a regular variation assumption, the dependence structure of the positive extremes is characterized by a measure, the spectral measure, defined on the positive orthant of the unit sphere. This measure gathers information on the localization of large events and has often a sparse support since such events do not simultaneously occur in all directions. However, it is defined via weak convergence which does not provide a natural way to capture this sparsity structure. In this talk, we introduce the notion of sparse regular variation which allows to better learn the tail structure of a random vector X. We use this concept in a statistical framework and provide a procedure which captures clusters of extremal coordinates of X. This approach also includes the identification of a threshold above which the values taken by X are considered as extreme. It leads to an efficient algorithm called MUSCLE. We illustrate our method on numerical experiments and wind speed data.

WEBINAIRE ouvert à toutes et tous : https://umontpellier-fr.zoom.us/j/85813807839