Spectral approximation of extremal dependence in high dimensions

This studentship will develop a paradigm-changing theoretical underpinning of novel tools for assessing extremal dependence in high dimensions. It is based on extending a recently discovered link between classical principal component analysis and multivariate extreme value theory.



While most statistical tools that have a strong theoretical underpinning characterise the typical behaviour of a system, in many practical or safety-critical situations it is instead the extreme behaviours and their dependence, which require particular attention. Contrary to public perception, examples of such settings are ubiquitous and an improved understanding aided by sound statistical procedures is of utmost importance, for instance to assess risk related to environmental hazards, network failure or financial portfolio losses. What complicates such tasks is the lack of generic and interpretable, theoretically well-studied and computationally feasible statistical tools to explore the extremal dependence structure of high-dimensional data.