Decompositions of dependence for high-dimensional extremes

We 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.


Published in:
Biometrika, 106, 3, 587-604
Year:
Sep 01 2019
Publisher:
Oxford, OXFORD UNIV PRESS
ISSN:
0006-3444
1464-3510
Keywords:
Laboratories:




 Record created 2019-11-12, last modified 2020-04-20


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