A geometric approach for multivariate extremal inference

Until recently, different types of joint tail dependence of random vectors required different modelling procedures, resulting in a lack of a unified approach for modelling multivariate extremes. A new development remedies this by using the geometry of the dataset to perform inference on the multivariate tail. A key quantity in this inference is the so-called "gauge function", whose values define this geometry.
In this talk, I'll present two methods to estimate the gauge function given data. The first relies on parametric assumptions on the form of the gauge function. The second is semi-parametric, interpolating the domain of the gauge function in a piecewise-linear fashion. 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 gauge function can be useful in defining a radial and an angular model, allowing for the joint fitting of extremal pseudo-polar coordinates. This new methodology is applied to environmental datasets, 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.