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On a nonparametric notion of residual and its applications


  • Patra, Rohit K.
  • Sen, Bodhisattva
  • Székely, Gábor J.


Given a random vector (X,Z), we define a notion of nonparametric residual of X on Z that is always independent of Z. Given (X,Y,Z), we use this notion of residual to develop a test for the conditional independence between X and Y, given Z.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:stapro:v:109:y:2016:i:c:p:208-213
    DOI: 10.1016/j.spl.2015.10.011

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    References listed on IDEAS

    1. Györfi, László & Walk, Harro, 2012. "Strongly consistent nonparametric tests of conditional independence," Statistics & Probability Letters, Elsevier, vol. 82(6), pages 1145-1150.
    2. 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.
    3. A. Sen & B. Sen, 2014. "Testing independence and goodness-of-fit in linear models," Biometrika, Biometrika Trust, vol. 101(4), pages 927-942.
    4. Pierre-Andre Chiappori & Bernard Salanie, 2000. "Testing for Asymmetric Information in Insurance Markets," Journal of Political Economy, University of Chicago Press, vol. 108(1), pages 56-78, February.
    5. Bodhisattva Sen & Probal Chaudhuri, 2012. "On Fractile Transformation of Covariates in Regression," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(497), pages 349-361, March.
    6. 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.
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