Characterizing extremal dependence on a hyperplane

Summary In this paper, we characterize the extremal dependence of d asymptotically dependent variables using a class of random vectors on the (d-1) -dimensional hyperplane perpendicular to the diagonal vector 1 = (1,… ,1). 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.