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A Szekely–Rizzo inequality for testing general copula homogeneity hypotheses

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  • Quessy, Jean-François

Abstract

This article extends to more than two vectors the popular moment inequality of Szekely and Rizzo and adapts it to test hypotheses about the copula of a multivariate population. The framework that is adopted is very general, as it allows one to test various kinds of hypotheses about the dependence structure of random vectors like symmetry, radial symmetry and equality of copulas. The proposed procedure is based on a V-statistic computed from the ranks of the observations. Its asymptotic distribution is derived under the null and general alternatives, and resampling is based on the multiplier bootstrap for degenerate V-statistics. A simulation study explores the sampling properties of the tests and compares with available methodologies.

Suggested Citation

  • Quessy, Jean-François, 2021. "A Szekely–Rizzo inequality for testing general copula homogeneity hypotheses," Journal of Multivariate Analysis, Elsevier, vol. 186(C).
    • Handle: RePEc:eee:jmvana:v:186:y:2021:i:c:s0047259x21000932
    DOI: 10.1016/j.jmva.2021.104815
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    References listed on IDEAS

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    1. Chen, Feifei & Meintanis, Simos G. & Zhu, Lixing, 2019. "On some characterizations and multidimensional criteria for testing homogeneity, symmetry and independence," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 125-144.
    2. Beare, Brendan K. & Seo, Juwon, 2020. "Randomization Tests Of Copula Symmetry," Econometric Theory, Cambridge University Press, vol. 36(6), pages 1025-1063, December.
    3. Rémillard, Bruno & Scaillet, Olivier, 2009. "Testing for equality between two copulas," Journal of Multivariate Analysis, Elsevier, vol. 100(3), pages 377-386, March.
    4. Dehling, H. & Mikosch, T., 1994. "Random Quadratic Forms and the Bootstrap for U-Statistics," Journal of Multivariate Analysis, Elsevier, vol. 51(2), pages 392-413, November.
    5. Niu, Cuizhen & Guo, Xu & Li, Yong & Zhu, Lixing, 2018. "Pairwise distance-based tests for conditional symmetry," Computational Statistics & Data Analysis, Elsevier, vol. 128(C), pages 145-162.
    6. Christian Genest & Johanna Nešlehová, 2014. "On tests of radial symmetry for bivariate copulas," Statistical Papers, Springer, vol. 55(4), pages 1107-1119, November.
    7. Tarik Bahraoui & Taoufik Bouezmarni & Jean†François Quessy, 2018. "A Family of Goodness†of†Fit Tests for Copulas Based on Characteristic Functions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 45(2), pages 301-323, June.
    8. Olivier Scaillet, 2005. "A Kolmogorov-Smirnov Type Test for Positive Quadrant Dependence," FAME Research Paper Series rp128, International Center for Financial Asset Management and Engineering.
    9. Christian Genest & Johanna Nešlehová & Jean-François Quessy, 2012. "Tests of symmetry for bivariate copulas," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(4), pages 811-834, August.
    10. Edward Frees & Emiliano Valdez, 1998. "Understanding Relationships Using Copulas," North American Actuarial Journal, Taylor & Francis Journals, vol. 2(1), pages 1-25.
    11. Pavel Krupskii, 2017. "Copula-based measures of reflection and permutation asymmetry and statistical tests," Statistical Papers, Springer, vol. 58(4), pages 1165-1187, December.
    12. Gabor J. Szekely & Maria L. Rizzo, 2005. "Hierarchical Clustering via Joint Between-Within Distances: Extending Ward's Minimum Variance Method," Journal of Classification, Springer;The Classification Society, vol. 22(2), pages 151-183, September.
    13. Szekely, Gábor J. & Rizzo, Maria L., 2005. "A new test for multivariate normality," Journal of Multivariate Analysis, Elsevier, vol. 93(1), pages 58-80, March.
    14. Michael Harder & Ulrich Stadtmüller, 2017. "Testing exchangeability of copulas in arbitrary dimension," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 29(1), pages 40-60, January.
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