Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Decompositions of Dependence for High-Dimensional Extremes   Employing the framework of regular variation, we propose two decompositions
which help to summarize and describel high-dimensional tail dependence. Via
transformation, we define a vector space on the positive orthant, yielding the
notion of basis. With a suitably-chosen transformation, we show that
transformed-linear operations applied to regularly varying random vectors
preserve regular variation. Rather than model regular-variation's angular
measure, we summarize tail dependence via a matrix of pairwise tail dependence
metrics. This matrix is positive semidefinite, and eigendecomposition allows
one to interpret tail dependence via the resulting eigenbasis. Additionally
this matrix is completely positive, and a resulting decomposition allows one to
easily construct regularly varying random vectors which share the same pairwise
tail dependencies. We illustrate our methods with Swiss rainfall data and
financial return data.

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The categories of this paper are: comp-gas
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The categories of this paper are: eess
34
The categories of this paper are: chem-ph
6
The categories of this paper are: astro-ph
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The categories of this paper are: econ
9
The categories of this paper are: nlin
12
The categories of this paper are: nucl-th
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-th
2
The categories of this paper are: math
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The categories of this paper are: math-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: physics
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-ph
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The categories of this paper are: solv-int