Modelling across extremal dependence classes

TL;DR

This paper introduces a unified model for bivariate extremes that covers both asymptotic dependence and independence, improving the flexibility and accuracy of extreme value analysis.

Contribution

A novel unified representation for bivariate extremes that applies across different dependence classes, addressing limitations of existing models.

Findings

Model performs well across various dependence scenarios.

Unified approach simplifies inference for extreme value dependence.

Applicable when at least one variable is large.

Abstract

Different dependence scenarios can arise in multivariate extremes, entailing careful selection of an appropriate class of models. In bivariate extremes, the variables are either asymptotically dependent or are asymptotically independent. Most available statistical models suit one or other of these cases, but not both, resulting in a stage in the inference that is unaccounted for, but can substantially impact subsequent extrapolation. Existing modelling solutions to this problem are either applicable only on sub-domains, or appeal to multiple limit theories. We introduce a unified representation for bivariate extremes that encompasses a wide variety of dependence scenarios, and applies when at least one variable is large. Our representation motivates a parametric model that encompasses both dependence classes. We implement a simple version of this model, and show that it performs well in a range of settings.