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Estimating a Multidimensional Extreme-Value Distribution

Author

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  • Einmahl, J. H. J.
  • Dehaan, L.
  • Huang, X.

Abstract

Let F and G be multivariate probability distribution functions, each with equal one dimensional marginals, such that there exists a sequence of constants an > 0, n [set membership, variant] , with [formula] for all continuity points (x1, ..., xd) of G. The distribution function G is characterized by the extreme-value index (determining the marginals) and the so-called angular measure (determining the dependence structure). In this paper, a non-parametric estimator of G, based on a random sample from F, is proposed. Consistency as well as asymptotic normality are proved under certain regularity conditions.

Suggested Citation

  • Einmahl, J. H. J. & Dehaan, L. & Huang, X., 1993. "Estimating a Multidimensional Extreme-Value Distribution," Journal of Multivariate Analysis, Elsevier, vol. 47(1), pages 35-47, October.
    • Handle: RePEc:eee:jmvana:v:47:y:1993:i:1:p:35-47
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    Cited by:

    1. Bücher Axel, 2014. "A note on nonparametric estimation of bivariate tail dependence," Statistics & Risk Modeling, De Gruyter, vol. 31(2), pages 1-12, June.
    2. Drees, Holger & Huang, Xin, 1998. "Best Attainable Rates of Convergence for Estimators of the Stable Tail Dependence Function," Journal of Multivariate Analysis, Elsevier, vol. 64(1), pages 25-47, January.
    3. Einmahl, John H.J. & de Haan, Laurens & Sinha, Ashoke Kumar, 1997. "Estimating the spectral measure of an extreme value distribution," Stochastic Processes and their Applications, Elsevier, vol. 70(2), pages 143-171, October.
    4. Frahm, Gabriel & Junker, Markus & Schmidt, Rafael, 2005. "Estimating the tail-dependence coefficient: Properties and pitfalls," Insurance: Mathematics and Economics, Elsevier, vol. 37(1), pages 80-100, August.
    5. Capéraà, Philippe & Fougères, Anne-Laure & Genest, Christian, 2000. "Bivariate Distributions with Given Extreme Value Attractor," Journal of Multivariate Analysis, Elsevier, vol. 72(1), pages 30-49, January.

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