# Modelling across extremal dependence classes

arXiv: https://arxiv.org/abs/1408.5060 · HTML: https://mlsanity.com/paper/1408.5060/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Aug 2014.

## Built on by (most cited first, 5 of 5)

- [Concentration bounds for the empirical angular measure with statistical learning applications](https://mlsanity.com/paper/2104.03966/) (2021)
- [Neural Bayes estimators for censored inference with peaks-over-threshold models](https://mlsanity.com/paper/2306.15642/) (2023)
- [Generative Machine Learning for Multivariate Angular Simulation](https://mlsanity.com/paper/2504.21505/) (2025)
- [Neural Bayes estimation and selection for complex bivariate extremal dependence models](https://mlsanity.com/paper/2503.23156/) (2025)
- [Modelling non-stationary extremal dependence through a geometric approach](https://mlsanity.com/paper/2509.22501/) (2025)

## Abstract (arXiv)

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.