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A moment-based test for extreme-value dependence

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  • Yeting Du
  • Johanna Nešlehová

Abstract

This paper proposes a new rank-based test of extreme-value dependence. The procedure is based on the first three moments of the bivariate probability integral transform of the underlying copula. It is seen that the test statistic is asymptotically normal and its finite- and large-sample variance are calculated explicitly. Consistent plug-in estimators for the variance are proposed, and a fast algorithm for their computation is given. Although it is shown via counterexamples that no test based on the probability integral transform can be consistent, the proposed procedure achieves good power against common alternatives, both in finite samples and asymptotically. Copyright Springer-Verlag 2013

Suggested Citation

  • Yeting Du & Johanna Nešlehová, 2013. "A moment-based test for extreme-value dependence," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 76(5), pages 673-695, July.
    • Handle: RePEc:spr:metrik:v:76:y:2013:i:5:p:673-695
    DOI: 10.1007/s00184-012-0410-z
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    References listed on IDEAS

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    1. Kojadinovic, Ivan & Yan, Jun, 2010. "Nonparametric rank-based tests of bivariate extreme-value dependence," Journal of Multivariate Analysis, Elsevier, vol. 101(9), pages 2234-2249, October.
    2. Kojadinovic, Ivan & Segers, Johan & Yan, Jun, 2011. "Large-sample tests of extreme-value dependence for multivariate copulas," LIDAM Reprints ISBA 2011025, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    3. Christian Genest & Johanna Nešlehová & Johanna Ziegel, 2011. "Rejoinder on: Inference in multivariate Archimedean copula models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(2), pages 290-292, August.
    4. Kojadinovic, Jean D. & Segers, Johan & Yan, Yun, 2011. "Large-sample tests of extreme-value dependence for multivariate copulas," LIDAM Discussion Papers ISBA 2011012, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    5. Nelsen, Roger B. & Quesada-Molina, José Juan & Rodríguez-Lallena, José Antonio & Úbeda-Flores, Manuel, 2003. "Kendall distribution functions," Statistics & Probability Letters, Elsevier, vol. 65(3), pages 263-268, November.
    6. Jean-François Quessy, 2012. "Testing for Bivariate Extreme Dependence Using Kendall's Process," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 39(3), pages 497-514, September.
    7. Christian Genest & Johanna Nešlehová & Johanna Ziegel, 2011. "Inference in multivariate Archimedean copula models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(2), pages 223-256, August.
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