Date: Wednesday, 30 October 2024, at 12.30pm (CET)

Dual format: ESSEC Paris La Défense (CNIT), Room TBA
and via Zoom, please click here

A geometric representation for multivariate extremes, based on the shapes of scaled sample clouds in light-tailed margins and their so-called limit sets, has recently been shown to connect several existing extremal dependence concepts. However, these results are purely probabilistic, and the geometric approach itself has not been fully exploited for statistical inference. We outline a method for parametric estimation of the limit set shape, which includes a useful non-/semi-parametric estimate as a pre-processing step. More fundamentally, our approach provides a new class of asymptotically motivated statistical models for the tails of multivariate distributions, and such models can accommodate any combination of simultaneous or non-simultaneous extremes through appropriate parametric forms for the limit set shape. In this talk we will also present ongoing work moving towards semiparametric methodology for greater flexibility. Extrapolation further into the tail of the distribution is possible via simulation from the fitted model, and probability estimates are possible in regions where other frameworks struggle. The methods are applied to river flow measurements in north-west England.

Kind regards,
Jeremy Heng, Olga Klopp, Roberto Reno, Marie Kratz and Riada Djebbar (Singapore Actuarial Society - ERM)