TY - JOUR

T1 - Determining the dependence structure of multivariate extremes

AU - Simpson, Emma

AU - Wadsworth, Jennifer

AU - Tawn, Jonathan

N1 - This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Biometrika following peer review. The definitive publisher-authenticated version E S Simpson, J L Wadsworth, J A Tawn, Determining the dependence structure of multivariate extremes, Biometrika 2020 107 (3): 513–532 is available online at: https://academic.oup.com/biomet/article-abstract/107/3/513/5831922?redirectedFrom=fulltext

PY - 2020/9/1

Y1 - 2020/9/1

N2 - In multivariate extreme value analysis, the nature of the extremal dependence between variables should be considered when selecting appropriate statistical models. Interest often lies in 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 nonstandard 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 utility 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 river flows in the U.K., estimating the probabilities of different subsets of sites being large simultaneously.

AB - In multivariate extreme value analysis, the nature of the extremal dependence between variables should be considered when selecting appropriate statistical models. Interest often lies in 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 nonstandard 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 utility 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 river flows in the U.K., estimating the probabilities of different subsets of sites being large simultaneously.

U2 - 10.1093/biomet/asaa018

DO - 10.1093/biomet/asaa018

M3 - Journal article

VL - 107

SP - 513

EP - 532

JO - Biometrika

JF - Biometrika

SN - 0006-3444

IS - 3

ER -