Cooley, D.Thibaud, E.2019-11-122019-11-122019-11-122019-09-0110.1093/biomet/asz028https://infoscience.epfl.ch/handle/20.500.14299/162856WOS:000493047200008We propose two decompositions that help to summarize and describe high-dimensional tail dependence within the framework of regular variation. We use a transformation to define a vector space on the positive orthant and show that transformed-linear operations applied to regularly-varying random vectors preserve regular variation. We summarize tail dependence via a matrix of pairwise tail dependence metrics that is positive semidefinite; eigendecomposition allows one to interpret tail dependence in terms of the resulting eigenbasis. This matrix is completely positive, and one can easily construct regularly-varying random vectors that share the same pairwise tail dependencies. We illustrate our methods with Swiss rainfall and financial returns data.BiologyMathematical & Computational BiologyStatistics & ProbabilityLife Sciences & Biomedicine - Other TopicsMathematical & Computational BiologyMathematicsangular measuredimension reductionregular variationtail dependencemultivariateindependenceinferencetext::journal::journal article::research article