Nonparametric tests for conditional independence in two-way contingency tables
(2010) Journal of Multivariate Analysis — Vol. 101, n° 4, p. 765-788 (2010)
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- 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. (C) 2010 Elsevier Inc. All rights reserved.
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Geenens, G., & Simar, L. (2010). Nonparametric tests for conditional independence in two-way contingency tables. Journal of Multivariate Analysis, 101(4), 765-788. https://doi.org/10.1016/j.jmva.2009.12.017 (Original work published 2010)