A geometric interpretation of multivariate extreme value analysis

par Ryan Campbell (Lancaster University)

mardi 17 juin 2025, 14:00 → 15:00 Europe/Paris

In extreme value analysis, interest lies in characterising the tail behaviour of random vectors. This is difficult, since different combinations of the vector's components can exhibit different tail dependence properties. In this talk, theory and methodology will be introduced to bypass these difficulties by studying the geometry of random vectors, with a view to perform inference on the multivariate tail. Two methods to estimate this geometry given data will be presented. The first relies on parametric assumptions. The second is semi-parametric, interpolating the domain of the underlying random vector in a piecewise-linear manner. This results in a simple construction that is flexible on data with extremal dependence behaviour that is difficult to parameterise, and is more suitable for higher-dimensional applications. The piecewise-linear approach can be useful in defining a radial and an angular model, allowing for the joint fitting of extremal pseudo-polar coordinates, a key feature of the geometric approach. The new methodology is applied to model high urban air pollution measurements, a setting where classical multivariate extremes methods often struggle due to the potential combination of dependence and independence in the joint tails.

Joint work with my PhD supervisor, Jennifer Wadsworth, at Lancaster University.