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Some New Copula Based Distribution-free Tests of Independence among Several Random Variables

Author

Listed:
  • Angshuman Roy

    (Indian Statistical Institute)

  • Anil K. Ghosh

    (Indian Statistical Institute)

  • Alok Goswami

    (Indian Statistical Institute)

  • C. A. Murthy

    (Indian Statistical Institute)

Abstract

Over the last couple of decades, several copula based methods have been proposed in the literature to test for independence among several random variables. But these existing tests are not invariant under monotone transformations of the variables, and they often perform poorly if the dependence among the variables is highly non-monotone in nature. In this article, we propose a copula based measure of dependency and use it to construct some distribution-free tests of independence. The proposed measure and the resulting tests, all are invariant under permutations and strictly monotone transformations of the variables. Our dependency measure involves a kernel function with an associated bandwidth parameter. We adopt a multi-scale approach, where we look at the results obtained for several choices of the bandwidth and aggregate them judiciously. Large sample properties of the dependency measure and the resulting tests are derived under appropriate regularity conditions. Several simulated and real data sets are analyzed to compare the performance of the proposed tests with some popular tests available in the literature.

Suggested Citation

  • Angshuman Roy & Anil K. Ghosh & Alok Goswami & C. A. Murthy, 2022. "Some New Copula Based Distribution-free Tests of Independence among Several Random Variables," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(2), pages 556-596, August.
    • Handle: RePEc:spr:sankha:v:84:y:2022:i:2:d:10.1007_s13171-020-00207-2
    DOI: 10.1007/s13171-020-00207-2
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    References listed on IDEAS

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    1. Taskinen, Sara & Kankainen, Annaliisa & Oja, Hannu, 2003. "Sign test of independence between two random vectors," Statistics & Probability Letters, Elsevier, vol. 62(1), pages 9-21, March.
    2. Manuel Úbeda-Flores, 2005. "Multivariate versions of Blomqvist’s beta and Spearman’s footrule," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 57(4), pages 781-788, December.
    3. Gaißer, Sandra & Ruppert, Martin & Schmid, Friedrich, 2010. "A multivariate version of Hoeffding's Phi-Square," Journal of Multivariate Analysis, Elsevier, vol. 101(10), pages 2571-2586, November.
    4. Fan, Yanan & de Micheaux, Pierre Lafaye & Penev, Spiridon & Salopek, Donna, 2017. "Multivariate nonparametric test of independence," Journal of Multivariate Analysis, Elsevier, vol. 153(C), pages 189-210.
    5. Taskinen, Sara & Oja, Hannu & Randles, Ronald H., 2005. "Multivariate Nonparametric Tests of Independence," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 916-925, September.
    6. Ruth Heller & Yair Heller & Malka Gorfine, 2013. "A consistent multivariate test of association based on ranks of distances," Biometrika, Biometrika Trust, vol. 100(2), pages 503-510.
    7. J. Cuesta-Albertos & M. Febrero-Bande, 2010. "A simple multiway ANOVA for functional data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 19(3), pages 537-557, November.
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