Title: Multivariate sparse clustering for extremes
Authors: Nicolas Meyer - Universite de Montpellier (France) [presenting]
Olivier Wintenberger - Sorbonne Universite (France)
Abstract: Identifying directions where extreme events occur is a major challenge in multivariate extreme value analysis. We use the concept of sparse regular variation introduced in previous work to infer the tail dependence of a random vector $X$. This approach relies on the Euclidean projection onto the simplex, which better exhibits the sparsity structure of the tail of $X$ than the standard methods. Our procedure, based on a rigorous methodology, aims at capturing clusters of extremal coordinates of $X$. It also includes the identification of the threshold above which the values taken by $X$ are considered as extreme. We provide an efficient and scalable algorithm called MUSCLE and apply it to numerical examples to highlight the relevance of our findings. Finally, we illustrate our approach with financial return data.