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A Method of Moments Estimator of Tail Dependence in Elliptical Copula Models

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  • Krajina, A.

    (Tilburg University, Center for Economic Research)

Abstract

An elliptical copula model is a distribution function whose copula is that of an elliptical distri- bution. The tail dependence function in such a bivariate model has a parametric representation with two parameters: a tail parameter and a correlation parameter. The correlation parameter can be estimated by robust methods based on the whole sample. Using the estimated correla- tion parameter as plug-in estimator, we then estimate the tail parameter applying a modification of the method of moments approach proposed in the paper by J.H.J. Einmahl, A. Krajina and J. Segers [Bernoulli 14(4), 2008, 1003-1026]. We show that such an estimator is consistent and asymptotically normal. Also, we derive the joint limit distribution of the estimators of the two parameters. By a simulation study, we illustrate the small sample behavior of the estimator of the tail parameter and we compare its performance to that of the estimator proposed in the paper by C. KlÄuppelberg, G. Kuhn and L. Peng [Scandinavian Journal of Statistics 35(4), 2008, 701-718].

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Bibliographic Info

Paper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 2009-42.

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Date of creation: 2009
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Handle: RePEc:dgr:kubcen:200942

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Web page: http://center.uvt.nl

Related research

Keywords: asymptotic normality; elliptical copula; elliptical distribution; meta-elliptical model; method of moments; semi-parametric model; tail dependence;

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References

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  1. Fang, Hong-Bin & Fang, Kai-Tai & Kotz, Samuel, 2002. "The Meta-elliptical Distributions with Given Marginals," Journal of Multivariate Analysis, Elsevier, vol. 82(1), pages 1-16, July.
  2. Einmahl, J.H.J. & Haan, L.F.M. de & Li, D., 2004. "Weighted Approximations of Tail Copula Processes with Application to Testing the Multivariate Extreme Value Condition," Discussion Paper 2004-71, Tilburg University, Center for Economic Research.
  3. Einmahl, J.H.J. & Krajina, A. & Segers, J.J.J., 2008. "A method of moments estimator of tail dependence," Open Access publications from Tilburg University urn:nbn:nl:ui:12-402837, Tilburg University.
  4. Asimit, Alexandru V. & Jones, Bruce L., 2007. "Extreme behavior of bivariate elliptical distributions," Insurance: Mathematics and Economics, Elsevier, vol. 41(1), pages 53-61, July.
  5. Claudia Klüppelberg & Gabriel Kuhn & Liang Peng, 2008. "Semi-Parametric Models for the Multivariate Tail Dependence Function - the Asymptotically Dependent Case," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 35(4), pages 701-718.
  6. Hashorva, Enkelejd, 2005. "Extremes of asymptotically spherical and elliptical random vectors," Insurance: Mathematics and Economics, Elsevier, vol. 36(3), pages 285-302, June.
  7. repec:sae:ecolab:v:16:y:2006:i:2:p:1-2 is not listed on IDEAS
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Cited by:
  1. Hashorva, Enkelejd, 2010. "On the residual dependence index of elliptical distributions," Statistics & Probability Letters, Elsevier, vol. 80(13-14), pages 1070-1078, July.

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