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Weak convergence of empirical and bootstrapped C-power processes and application to copula goodness-of-fit

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  • Quessy, Jean-François
  • Bahraoui, Tarik

Abstract

The selection of a copula that appropriately describes the dependence structure of a bivariate distribution function is an issue of a prime interest in multivariate statistical analysis. The most popular methods of testing are those based on the empirical copula and on Kendall’s process; these tests require the use of the parametric bootstrap, which is computationally heavy. This paper introduces the concept of C-power functions associated to bivariate copulas. In the first step, their theoretical properties are explored and computations for many popular dependence models are provided. Then, empirical counterparts of these functions are proposed and the weak convergence of suitably normalized versions is obtained from an application of the functional delta method. In addition, a multiplier bootstrap method for these C-power processes is described and validated. While of an independent interest to treat many hypotheses related to copulas, these newly introduced tools are used to develop a goodness-of-fit test for bivariate multi-parameter copula models. The recursive nature of the C-power functions induces easily computable formulas for the test statistics and suggests a sequential method of testing. The sample properties of this goodness-of-fit test are investigated and compared to those of competing procedures, and its usefulness is illustrated on some pairs of the multivariate Uranium exploration data set.

Suggested Citation

  • Quessy, Jean-François & Bahraoui, Tarik, 2014. "Weak convergence of empirical and bootstrapped C-power processes and application to copula goodness-of-fit," Journal of Multivariate Analysis, Elsevier, vol. 129(C), pages 16-36.
    • Handle: RePEc:eee:jmvana:v:129:y:2014:i:c:p:16-36
    DOI: 10.1016/j.jmva.2014.03.018
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    References listed on IDEAS

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    1. Nelsen, Roger B., 1997. "Dependence and Order in Families of Archimedean Copulas," Journal of Multivariate Analysis, Elsevier, vol. 60(1), pages 111-122, January.
    2. Christian Genest & Jean‐François Quessy & Bruno Rémillard, 2006. "Goodness‐of‐fit Procedures for Copula Models Based on the Probability Integral Transformation," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 33(2), pages 337-366, June.
    3. Segers, Johan, 2012. "Asymptotics of empirical copula processes under non-restrictive smoothness assumptions," LIDAM Reprints ISBA 2012009, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    4. 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.
    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.
    6. Genest, Christian & Rémillard, Bruno & Beaudoin, David, 2009. "Goodness-of-fit tests for copulas: A review and a power study," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 199-213, April.
    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.
    8. Genest, Christian & Rivest, Louis-Paul, 2001. "On the multivariate probability integral transformation," Statistics & Probability Letters, Elsevier, vol. 53(4), pages 391-399, July.
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