The angular measure for multivariate extremes : concentration bounds, goodness-of-fit tests, and generative methods
(2025)
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- Authors
- Supervisors
- Segers, Johan
- Abstract
- Extreme value analysis is a branch of statistics concerned with modeling the extreme behavior of random phenomena. In many real-world systems—such as insurance portfolios, transportation networks, or financial markets—multiple components may simultaneously exhibit extreme behavior due to underlying dependencies. Accurately modeling this joint tail behavior is therefore of primary importance and requires specific mathematical tools. A central object in this theory is the angular measure, which captures the extremal dependence structure among the components. This thesis aims to advance our understanding of the statistical estimation of the angular measure from several perspectives. The first part of the work focuses on deriving finite-sample guarantees for the empirical angular measure obtained from a random sample. These results are particularly useful for establishing theoretical guarantees for various statistical learning procedures that rely on this widely used estimator. The second part addresses the bivariate case, where asymptotic analysis of the empirical angular measure is tractable. It leads to the development of powerful goodness-of-fit tests for parametric models of the angular measure that are popular in applied contexts. Finally, the third part explores the use of generative adversarial networks (GANs) to indirectly model the angular measure by providing a sampling algorithm. It also discusses the specific challenges associated with applying generative approaches in this setting.
- Affiliations
Citations
Lhaut, S. (2025). The angular measure for multivariate extremes : concentration bounds, goodness-of-fit tests, and generative methods. https://hdl.handle.net/2078.5/259690