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A sum characterization of hidden regular variation with likelihood inference via expectation-maximization

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  • Grant B. Weller
  • Daniel Cooley

Abstract

A fundamental deficiency of classical multivariate extreme value theory is the inability to distinguish between asymptotic independence and exact independence. In this work, we examine multivariate threshold modelling in the framework of regular variation on cones. Tail dependence is described by a limiting measure, which in some cases is degenerate on joint tail regions despite strong subasymptotic dependence in such regions. Hidden regular variation, a higher-order tail decay on these regions, offers a refinement of the classical theory. We develop a representation of random vectors possessing hidden regular variation as the sum of independent regular varying components. The representation is shown to be asymptotically valid via a multivariate tail equivalence result. We develop a likelihood-based estimation procedure from this representation via a Monte Carlo expectation-maximization algorithm which has been modified for tail estimation. The method is demonstrated on simulated data and applied to air pollution measurements.

Suggested Citation

  • Grant B. Weller & Daniel Cooley, 2014. "A sum characterization of hidden regular variation with likelihood inference via expectation-maximization," Biometrika, Biometrika Trust, vol. 101(1), pages 17-36.
    • Handle: RePEc:oup:biomet:v:101:y:2014:i:1:p:17-36.
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    File URL: http://hdl.handle.net/10.1093/biomet/ast046
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    Cited by:

    1. Bikramjit Das & Marie Kratz, 2017. "Diversification benefits under multivariate second order regular variation," Working Papers hal-01520655, HAL.
    2. Das, Bikramjit & Fasen-Hartmann, Vicky, 2018. "Risk contagion under regular variation and asymptotic tail independence," Journal of Multivariate Analysis, Elsevier, vol. 165(C), pages 194-215.
    3. Das, Bikramjit & Kratz, Marie, 2017. "Diversification benefits under multivariate second order regular variation," ESSEC Working Papers WP1706, ESSEC Research Center, ESSEC Business School.
    4. Das Bikramjit & Fasen-Hartmann Vicky, 2019. "Conditional excess risk measures and multivariate regular variation," Statistics & Risk Modeling, De Gruyter, vol. 36(1-4), pages 1-23, December.
    5. Tankov, Peter, 2016. "Tails of weakly dependent random vectors," Journal of Multivariate Analysis, Elsevier, vol. 145(C), pages 73-86.
    6. Bikramjit Das & Vicky Fasen, 2016. "Risk contagion under regular variation and asymptotic tail independence," Papers 1603.09406, arXiv.org, revised Apr 2017.

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