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An M-estimator for tail dependence in arbitrary dimensions

Author

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  • Einmahl, John H. J.
  • Krajina, Andrea
  • Segers, Johan

Abstract

Consider a random sample in the max-domain of attraction of a multivariate extreme value distribution such that the dependence structure of the attractor belongs to a parametric model. A new estimator for the unknown parameter is defined as the value that minimizes the distance between a vector of weighted integrals of the tail dependence function and their empirical counterparts. The minimization problem has, with probability tending to one, a unique, global solution. The estimator is consistent and asymptotically normal. The spectral measures of the tail dependence models to which the method applies can be discrete or continuous. Examples demonstrate the applicability and the performance of the method.
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Suggested Citation

  • Einmahl, John H. J. & Krajina, Andrea & Segers, Johan, 2012. "An M-estimator for tail dependence in arbitrary dimensions," LIDAM Reprints ISBA 2012035, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    • Handle: RePEc:aiz:louvar:2012035
    Note: In : The Annals of Statistics, vol. 40, no.3, p. 1764-1793 (2012)
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    References listed on IDEAS

    as
    1. Einmahl, J.H.J. & Krajina, A. & Segers, J.J.J., 2007. "A Method of Moments Estimator of Tail Dependence," Discussion Paper 2007-80, Tilburg University, Center for Economic Research.
    2. Einmahl, John H. J., 1997. "Poisson and Gaussian approximation of weighted local empirical processes," Stochastic Processes and their Applications, Elsevier, vol. 70(1), pages 31-58, October.
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    10. Guillotte, Simon & Perron, Francois & Segers, Johan, 2011. "Non-parametric Bayesian inference on bivariate extremes," LIDAM Reprints ISBA 2011011, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
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    More about this item

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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