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Maximally selected chi-square statistics and binary splits of nominal variables
1Department of Medical Statistics and Epidemiology, Technical University of Munich, Ismaningerstr. 22, D-81675 Munich, Germany. anne-laure.boulesteix@tum.de
Abstract:
We address the problem of maximally selected chi-square statistics in the case of a binary Y variable and a nominal X variable with several categories. The distribution of the maximally selected chi-square statistic has already been derived when the best cutpoint is chosen from a continuous or an ordinal X, but not when the best split is chosen from a nominal X. In this paper, we derive the exact distribution of the maximally selected chi-square statistic in this case using a combinatorial approach. Applications of the derived distribution to variable selection and hypothesis testing are discussed based on simulations. As an illustration, our method is applied to a birth data set.
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