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Strongly consistent nonparametric tests of conditional independence

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  • Györfi, László
  • Walk, Harro
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    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.

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    File URL: http://www.sciencedirect.com/science/article/pii/S0167715212000703
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    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 82 (2012)
    Issue (Month): 6 ()
    Pages: 1145-1150

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    Handle: RePEc:eee:stapro:v:82:y:2012:i:6:p:1145-1150

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    Related research

    Keywords: Conditional independence; Nonparametric test; Partition; Distribution-free strong consistency;

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    1. 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.
    2. 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.
    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. De Wet, T., 1980. "Cramér-von Mises tests for independence," Journal of Multivariate Analysis, Elsevier, vol. 10(1), pages 38-50, March.
    5. Su, Liangjun & White, Halbert, 2008. "A Nonparametric Hellinger Metric Test For Conditional Independence," Econometric Theory, Cambridge University Press, vol. 24(04), pages 829-864, August.
    6. Csörgo, Sándor, 1985. "Testing for independence by the empirical characteristic function," Journal of Multivariate Analysis, Elsevier, vol. 16(3), pages 290-299, June.
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