Determining the Dependence Structure of Multivariate Extremes

TL;DR

This paper introduces new indices based on hidden regular variation to analyze the extremal dependence structure in multivariate data, providing novel insights and inference methods for understanding simultaneous extremes.

Contribution

It develops a new set of indices for extremal dependence analysis using hidden regular variation on non-standard cones, enhancing the understanding of multivariate extremes.

Findings

New indices reveal previously unmeasurable dependence aspects.

Application to UK river flows demonstrates practical utility.

Methods estimate probabilities of simultaneous large values.

Abstract

In multivariate extreme value analysis, the nature of the extremal dependence between variables should be considered when selecting appropriate statistical models. Interest often lies with determining which subsets of variables can take their largest values simultaneously, while the others are of smaller order. Our approach to this problem exploits hidden regular variation properties on a collection of non-standard cones and provides a new set of indices that reveal aspects of the extremal dependence structure not available through existing measures of dependence. We derive theoretical properties of these indices, demonstrate their value through a series of examples, and develop methods of inference that also estimate the proportion of extremal mass associated with each cone. We apply the methods to UK river flows, estimating the probabilities of different subsets of sites being large simultaneously.