Multivariate Sparse Clustering for Extremes

Identifying directions where extreme events occur is a significant challenge in multivariate extreme value analysis. In this article, we use the concept of sparse regular variation introduced by Meyer and Wintenberger 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 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. Supplementary materials for this article are available online.