Higher order tail densities of copulas and hidden regular variation

Haijun Li; Lei Hua

doi:10.1016/j.jmva.2014.12.010

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Higher order tail densities of copulas and hidden regular variation

Journal article

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Peer reviewed

Higher order tail densities of copulas and hidden regular variation

Haijun Li and Lei Hua

Journal of multivariate analysis, Vol.138, pp.143-155

06/2015

DOI: https://doi.org/10.1016/j.jmva.2014.12.010

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https://hdl.handle.net/2376/112685

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Abstract

Tail dependence

Multivariate regular variation

Upper exponent function

Tail order function

A notion of higher order tail densities for copulas is introduced using multivariate regular variation of copula densities, and densities of multivariate extremes with various margins can then be studied in a unified fashion. We show that the tail of a multivariate density can be decomposed into the tail density of the underlying copula, coupled with marginal tail transforms of the three types: Fréchet, Gumbel, and Weibull types. We also derive the relation between the tail density and tail order functions of a copula in the context of hidden regular variation. Some illustrative examples are given.

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Title: Higher order tail densities of copulas and hidden regular variation
Creators: Haijun Li - Department of Mathematics, Washington State University, Pullman, WA, 99164, USA
Lei Hua - Division of Statistics, Northern Illinois University, DeKalb, IL, 60115, USA
Publication Details: Journal of multivariate analysis, Vol.138, pp.143-155
Academic Unit: Mathematics and Statistics, Department of
Publisher: Elsevier Inc
Identifiers: 99900547545401842
Language: English
Resource Type: Journal article