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March 2014 Relations between hidden regular variation and the tail order of copulas
Lei Hua, Harry Joe, Haijun Li
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J. Appl. Probab. 51(1): 37-57 (March 2014). DOI: 10.1239/jap/1395771412

Abstract

We study the relations between the tail order of copulas and hidden regular variation (HRV) on subcones generated by order statistics. Multivariate regular variation (MRV) and HRV deal with extremal dependence of random vectors with Pareto-like univariate margins. Alternatively, if one uses a copula to model the dependence structure of a random vector then the upper exponent and tail order functions can be used to capture the extremal dependence structure. After defining upper exponent functions on a series of subcones, we establish the relation between the tail order of a copula and the tail indexes for MRV and HRV. We show that upper exponent functions of a copula and intensity measures of MRV/HRV can be represented by each other, and the upper exponent function on subcones can be expressed by a Pickands-type integral representation. Finally, a mixture model is given with the mixing random vector leading to the finite-directional measure in a product-measure representation of HRV intensity measures.

Citation

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Lei Hua. Harry Joe. Haijun Li. "Relations between hidden regular variation and the tail order of copulas." J. Appl. Probab. 51 (1) 37 - 57, March 2014. https://doi.org/10.1239/jap/1395771412

Information

Published: March 2014
First available in Project Euclid: 25 March 2014

zbMATH: 1294.62131
MathSciNet: MR3189440
Digital Object Identifier: 10.1239/jap/1395771412

Subjects:
Primary: 62H20

Rights: Copyright © 2014 Applied Probability Trust

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Vol.51 • No. 1 • March 2014
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