Statistics and Data Science seminars: Lambert De Monte (The University of Edinburgh)

Extreme events, whether of environmental, biological, or financial nature, only to name a few, pose recurring risk to our society and daily lives. Accurate and reliable assessment of their likelihood or frequency of occurrence allows for better planning, mitigation, and adaptation efforts. The mathematical framework of extreme value theory provides a principled approach to fulfilling this aim via the characterisation, assessment, and quantification of the risk of extreme events of possibly yet-unobserved magnitudes.

The geometric approach to multivariate extreme value theory (MEVT) arises via the study of suitably scaled sample clouds―or suitably scaled independent observations from random vectors―and their convergence in probability onto compact and starshaped limit sets. A recent revisit of this probabilistic framework lead to meaningful developments in the field of statistical inference for multivariate extremes.

In this presentation, we discuss a new method for the statistical inference of multivariate extremes relying on a radial-angular decomposition of a random vector of interest: we consider the distribution of radial exceedances of a high conditional quantile of the distribution of radii given their angles (or directions). The conditional quantile surface as well as the density of the directions can be interpreted as starshaped sets which, along with the above-mentioned to perform statistical inference for new multivariate extremes models. An application to environmental data will be discussed.

Joint work with Raphaël Huser, Jordan Richards, and Ioannis Papastathopoulos.