Nonparametric tests for conditional independence in two-way contingency tables |
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Authors: | Gery Geenens Léopold Simar |
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Institution: | a Institut de Statistique, Université catholique de Louvain, Belgium b Department of Mathematics and Statistics, University of Melbourne, Australia |
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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. |
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Keywords: | primary 62H17 62G08 secondary 62H20 62G10 |
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