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Dependence properties of multivariate max-stable distributions

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  • Papastathopoulos, Ioannis
  • Tawn, Jonathan A.

Abstract

For an m-dimensional multivariate extreme value distribution there exist 2m−1 exponent measures which are linked and completely characterise the dependence of the distribution and all of its lower dimensional margins. In this paper we generalise the inequalities of Schlather and Tawn (2002) for the sets of extremal coefficients and construct bounds that higher order exponent measures need to satisfy to be consistent with lower order exponent measures. Subsequently we construct nonparametric estimators of the exponent measures which impose, through a likelihood-based procedure, the new dependence constraints and provide an improvement on the unconstrained estimators.

Suggested Citation

  • Papastathopoulos, Ioannis & Tawn, Jonathan A., 2014. "Dependence properties of multivariate max-stable distributions," Journal of Multivariate Analysis, Elsevier, vol. 130(C), pages 134-140.
    • Handle: RePEc:eee:jmvana:v:130:y:2014:i:c:p:134-140
    DOI: 10.1016/j.jmva.2014.05.001
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    References listed on IDEAS

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    1. Deheuvels, Paul, 1991. "On the limiting behavior of the Pickands estimator for bivariate extreme-value distributions," Statistics & Probability Letters, Elsevier, vol. 12(5), pages 429-439, November.
    2. Martin Schlather, 2003. "A dependence measure for multivariate and spatial extreme values: Properties and inference," Biometrika, Biometrika Trust, vol. 90(1), pages 139-156, March.
    3. Zhang, Dabao & Wells, Martin T. & Peng, Liang, 2008. "Nonparametric estimation of the dependence function for a multivariate extreme value distribution," Journal of Multivariate Analysis, Elsevier, vol. 99(4), pages 577-588, April.
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    Cited by:

    1. Papastathopoulos, Ioannis & Strokorb, Kirstin, 2016. "Conditional independence among max-stable laws," Statistics & Probability Letters, Elsevier, vol. 108(C), pages 9-15.

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