Determining the Dependence Structure of Multivariate Extremes

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.

References in corpus (2)

• Max-stable models for multivariate extremes
• Sparse Representation of Multivariate Extremes with Applications to Anomaly Ranking

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• A Multivariate Extreme Value Theory Approach to Anomaly Clustering and Visualization
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• Simulating flood event sets using extremal principal components
• Estimating the limiting shape of bivariate scaled sample clouds: with additional benefits of self-consistent inference for existing extremal dependence properties
• Sparse regular variation
• Tail inverse regression for dimension reduction with extreme response
• Hidden tail chains and recurrence equations for dependence parameters associated with extremes of higher-order Markov chains
• Spectral learning of multivariate extremes