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Strongly consistent nonparametric tests of conditional independence

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  • Györfi, László
  • Walk, Harro

Abstract

A simple and explicit procedure for testing the conditional independence of two multi-dimensional random variables given a third random vector is described. The associated L1-based test statistic is defined for when the empirical distribution of the variables is restricted to finite partitions. Distribution-free strong consistency is proved.

Suggested Citation

  • Györfi, László & Walk, Harro, 2012. "Strongly consistent nonparametric tests of conditional independence," Statistics & Probability Letters, Elsevier, vol. 82(6), pages 1145-1150.
    • Handle: RePEc:eee:stapro:v:82:y:2012:i:6:p:1145-1150
    DOI: 10.1016/j.spl.2012.02.023
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    References listed on IDEAS

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    1. Bakirov, Nail K. & Rizzo, Maria L. & Szekely, Gábor J., 2006. "A multivariate nonparametric test of independence," Journal of Multivariate Analysis, Elsevier, vol. 97(8), pages 1742-1756, September.
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    3. Oliver Linton & Pedro Gozalo, 1996. "Conditional Independence Restrictions: Testing and Estimation," Cowles Foundation Discussion Papers 1140, Cowles Foundation for Research in Economics, Yale University.
    4. Su, Liangjun & White, Halbert, 2008. "A Nonparametric Hellinger Metric Test For Conditional Independence," Econometric Theory, Cambridge University Press, vol. 24(4), pages 829-864, August.
    5. Beran, R. & Bilodeau, M. & Lafaye de Micheaux, P., 2007. "Nonparametric tests of independence between random vectors," Journal of Multivariate Analysis, Elsevier, vol. 98(9), pages 1805-1824, October.
    6. Csörgo, Sándor, 1985. "Testing for independence by the empirical characteristic function," Journal of Multivariate Analysis, Elsevier, vol. 16(3), pages 290-299, June.
    7. Cotterill Derek S. & Csörgö Miklós, 1985. "On The Limiting Distribution Of And Critical Values For The Hoeffding, Blum, Kiefer, Rosenblatt Independence Criterion," Statistics & Risk Modeling, De Gruyter, vol. 3(1-2), pages 1-48, February.
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    Cited by:

    1. Lorenzo Frattarolo & Dominique Guegan, 2013. "Empirical Projected Copula Process and Conditional Independence an Extended Version," Documents de travail du Centre d'Economie de la Sorbonne 13068, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    2. Lorenzo Frattarolo & Dominique Guegan, 2013. "Empirical Projected Copula Process and Conditional Independence An Extended Version," Post-Print halshs-00881185, HAL.
    3. Patra, Rohit K. & Sen, Bodhisattva & Székely, Gábor J., 2016. "On a nonparametric notion of residual and its applications," Statistics & Probability Letters, Elsevier, vol. 109(C), pages 208-213.

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