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Multivariate threshold exceedances and extremal graphical models in the presence of multiple extreme directions by Anas MOURAHIB -
Lundi 18/08/2025 à 16h00 - Auditoire MORE51 - Place Montesquieu, 2 - 1348 Louvain-la-Neuve -
Consider a random vector representing risk factors and suppose that we are interested in extreme scenarios. The threshold exceedances method is widely used in extreme value theory. It uses the fact that asymptotically, exceedances over a high threshold can be modelled using a multivariate generalized Pareto distribution. In the literature, statistical practice of this method has been discussed only when all risks are large simultaneously. This condition is not realistic for example when some of the risks are nearly independent. To address this limitation, we first develop a parametric model that accommodates cases where only some risk factors are extreme while others remain moderate. We introduce the concept of extreme directions to describe these cases and prove that our construction encompasses the full range of possible max-stable dependence structures. Second, we propose an estimation procedure for this model, leading to an algorithm capable of identifying extreme directions. Finally, we extend the framework of extremal graphical models by incorporating both multiple extreme directions and extremal independence, offering a more flexible and realistic approach to modeling extreme events.
Jury members :
Prof. Segers Johan (UCLouvain) (Supervisor)
Prof. Kiriliouk Anna (University of Namur, Belg.) (Supervisor)
Prof. Denuit Michel (UCLouvain) (Chairperson)
Prof. Pircalabelu Eugen (UCLouvain) (Secretary)
Prof. Engelke Sebastian (University of Geneva, C.H.)
Prof. Röttger Frank (Eindhoven University of Technology, N.L.)
Pay attention : the public defense of Anas MOURAHIB will also take place in the form of a videoconference
