Novel estimation procedures for dependence in multivariate extremes

Project ID: 2228cd1426 (You will need this ID for your application)

UCL Lead department: Statistical Science

Project Summary:

Extreme value analysis is the statistical study of unusually large or small values; often extrapolating to events not previously observed using theoretically justified methodology. In environmental settings, applications include heavy rainfall, high winds, or low temperatures, with the aim of mitigating the impact of future extreme events.

In a multivariate setting, the aim is to study extreme values across several variables. This is important since their consequences can be even more severe than for one variable individually. Extremes may tend to occur simultaneously or separately across the variables, or there may be a more complicated structure involving a mixture of these features. Appropriate model selection is therefore crucial for reliable estimation of joint extreme events.

There are various frameworks available to assess and model extremal dependence. However, separate inference under these individual frameworks can yield inconsistent conclusions about the extremal dependence behaviour. Recent theoretical developments have found links between different representations of extremal dependence, and work by Simpson and Tawn (2022) exploits these theoretical results for inferential purposes, but is limited to the bivariate case. Extensions of this approach to allow for higher dimensional inference will be considered during this PhD project, where consistency across dimension becomes an additional consideration. There is also scope to study other aspects of multivariate extremal dependence, depending on the student’s interests.

The student will study the mathematical theory behind extreme value analysis and work on developing their own inferential approaches to allow for consistent and reliable estimation of extremal dependence features. A student with a strong mathematical background, good programming skills, and a keen interest in developing novel statistical methodology would be ideally suited to this project.

Simpson, E. S. and Tawn, J. A. (2022). Estimating the limiting shape of bivariate scaled sample clouds for self-consistent inference of extremal dependence properties. arXiv:2207.02626.