Nonparametric tests for conditional independence in two-way contingency tables

Testing for the independence between two categorical variables RR and SS 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 pp characteristics is also observed. Those explanatory variables, likely to be associated with RR and SS, can play a major role in their possible association, and it can therefore be interesting to test the independence between RR and SS 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.