Decompositions of dependence for high-dimensional extremes

By Daniel Cooley, Emeric Thibaud. Biometrika, 2016

104 citations recorded by the source corpus.

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.

Subfields: Finance, Global and Planetary Change

View Paper: https://www.semanticscholar.org/paper/7dd88836b7d28660acfcdd4dc51bddc9401162ef

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Citations in the corpus

Functional peaks‐over‐threshold analysis (2020, background): “, 1993) or via a methodology tailored for extremes (Cooley and Thibaud, 2019), which could help in studying weather patterns such the North American winter dipole (Wang et al.”
Graphical models for extremes (2018, methodology): “Other approaches include constructions through factor copulas (Lee and Joe, 2018), ensembles of trees combining bivariate copulas (Yu et al., 2017), graphical models for large censored observations (Hitz and Evans, 2016) and eigendecompositions (Cooley and Thibaud, 2019).”