Determining the Dependence Structure of Multivariate Extremes
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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 is based on exploiting hidden regular variation properties on a collection of non-standard cones. This provides a new set of indices that reveal aspects of the extremal dependence structure not available through any existing measures of dependence. We derive theoretical properties of these indices, demonstrate their value through a series of examples, and develop methods of inference which also estimate the proportion of extremal mass associated with each cone. We consider two inferential approaches: in the first, we approximate the cones via a truncation of the variables; the second involves partitioning the simplex associated with their radial-angular components. We apply the methods to UK river flows, estimating the probabilities of different subsets of sites being simultaneously large.
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