Wan, P. (2026). Characterizing extremal dependence on a hyperplane Biometrika, 113(2).
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Affiliated author
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Publication year2026
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JournalBiometrika
Summary: In this paper, we characterize the extremal dependence of (Formula presented) asymptotically dependent variables using a class of random vectors on the (Formula presented) -dimensional hyperplane perpendicular to the diagonal vector (Formula presented). This translates analyses of multivariate extremes to analyses on a linear vector space, opening up possibilities for applying existing statistical techniques based on linear operations. As an example, we demonstrate how to obtain lower-dimensional approximations of tail dependence through principal component analysis. Additionally, we show that the widely used Hüsler–Reiss family is characterized by a Gaussian family residing on the hyperplane.