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 which we illustrate on numerical experiments. We end our presentation with an application to extreme variability for financial data.
The talk is based on two papers written in collaboration with N. Meyer (IMAG, University of Montpellier):
- Multivariate sparse clustering for extremes (2020+): https://arxiv.org/abs/2007.11848
- Sparse regular variation (2021) Advances in Applied Probability, Vol. 53, no. 4.
Personal Website of Olivier Wintenberger
The talk also can be joined online via our ZOOM MEETING
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