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A consistent multivariate test of association based on ranks of distances

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  • Ruth Heller
  • Yair Heller
  • Malka Gorfine

Abstract

We consider the problem of detecting associations between random vectors of any dimension. Few tests of independence exist that are consistent against all dependent alternatives. We propose a powerful test that is applicable in all dimensions and consistent against all alternatives. The test has a simple form, is easy to implement, and has good power. Copyright 2013, Oxford University Press.

Suggested Citation

  • 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.
    • Handle: RePEc:oup:biomet:v:100:y:2013:i:2:p:503-510
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    File URL: http://hdl.handle.net/10.1093/biomet/ass070
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    Citations

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    Cited by:

    1. S Gorsky & L Ma, 2022. "Multi-scale Fisher’s independence test for multivariate dependence [A simple measure of conditional dependence]," Biometrika, Biometrika Trust, vol. 109(3), pages 569-587.
    2. Roy, Angshuman & Ghosh, Anil K., 2020. "Some tests of independence based on maximum mean discrepancy and ranks of nearest neighbors," Statistics & Probability Letters, Elsevier, vol. 164(C).
    3. Cui, Hengjian & Zhong, Wei, 2019. "A distribution-free test of independence based on mean variance index," Computational Statistics & Data Analysis, Elsevier, vol. 139(C), pages 117-133.
    4. L Weihs & M Drton & N Meinshausen, 2018. "Symmetric rank covariances: a generalized framework for nonparametric measures of dependence," Biometrika, Biometrika Trust, vol. 105(3), pages 547-562.
    5. Ćmiel, Bogdan & Ledwina, Teresa, 2020. "Validation of association," Insurance: Mathematics and Economics, Elsevier, vol. 91(C), pages 55-67.
    6. Alexander S. Long & Brian J. Reich & Ana‐Maria Staicu & John Meitzen, 2023. "A nonparametric test of group distributional differences for hierarchically clustered functional data," Biometrics, The International Biometric Society, vol. 79(4), pages 3778-3791, December.
    7. Cencheng Shen & Joshua T. Vogelstein, 2021. "The exact equivalence of distance and kernel methods in hypothesis testing," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 105(3), pages 385-403, September.
    8. Hongjian Shi & Marc Hallin & Mathias Drton & Fang Han, 2020. "Rate-Optimality of Consistent Distribution-Free Tests of Independence Based on Center-Outward Ranks and Signs," Working Papers ECARES 2020-23, ULB -- Universite Libre de Bruxelles.
    9. Ma, Zichen & Hanson, Timothy E., 2020. "Bayesian nonparametric test for independence between random vectors," Computational Statistics & Data Analysis, Elsevier, vol. 149(C).
    10. 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.
    11. 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.

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