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Nonparametric tests for conditional independence in two-way contingency tables

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  • Geenens, Gery
  • Simar, Léopold

Abstract

Testing for the independence between two categorical variables R and S forming a contingency table is a well-known problem: the classical chi-square and likelihood ratio tests are used. Suppose now that for each individual a set of p characteristics is also observed. Those explanatory variables, likely to be associated with R and S, can play a major role in their possible association, and it can therefore be interesting to test the independence between R and S conditionally on them. In this paper, we propose two nonparametric tests which generalise the chi-square and the likelihood ratio ideas to this case. The procedure is based on a kernel estimator of the conditional probabilities. The asymptotic law of the proposed test statistics under the conditional independence hypothesis is derived; the finite sample behaviour of the procedure is analysed through some Monte Carlo experiments and the approach is illustrated with a real data example.

Suggested Citation

  • Geenens, Gery & Simar, Léopold, 2010. "Nonparametric tests for conditional independence in two-way contingency tables," Journal of Multivariate Analysis, Elsevier, vol. 101(4), pages 765-788, April.
  • Handle: RePEc:eee:jmvana:v:101:y:2010:i:4:p:765-788
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    References listed on IDEAS

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    1. Romano, Joseph P. & Wolf, Michael, 2000. "A more general central limit theorem for m-dependent random variables with unbounded m," Statistics & Probability Letters, Elsevier, vol. 47(2), pages 115-124, April.
    2. Signorini, D.F. & Jones, M.C., 2004. "Kernel Estimators for Univariate Binary Regression," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 119-126, January.
    3. Rodriguez-Campos, M. C. & Cao-Abad, R., 1993. "Nonparametric bootstrap confidence intervals for discrete regression functions," Journal of Econometrics, Elsevier, vol. 58(1-2), pages 207-222, July.
    4. Rodriguez-Campos, M. Celia, 1999. "On Confidence Intervals in Nonparametric Binary Regression via Edgeworth Expansions," Journal of Multivariate Analysis, Elsevier, vol. 69(2), pages 218-241, May.
    5. Joel L. Horowitz & N. E. Savin, 2001. "Binary Response Models: Logits, Probits and Semiparametrics," Journal of Economic Perspectives, American Economic Association, vol. 15(4), pages 43-56, Fall.
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    Cited by:

    1. Geenens Gery, 2010. "Who Deserved the 2008-2009 Belgian Football Champion Title? A Semiparametric Answer," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 6(4), pages 1-31, October.
    2. Hui, Francis K.C. & Geenens, Gery, 2012. "Nonparametric bootstrap tests of conditional independence in two-way contingency tables," Journal of Multivariate Analysis, Elsevier, vol. 112(C), pages 130-144.

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