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Boulesteix, Anne-Laure
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Discussion paper // Sonderforschungsbereich 386 der Ludwig-Maximilians-Universität München 449
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 pregnancy and birth data set.
Categorical variables
association test
contingency table
exact distribution
variable selection
selection bias
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Working Paper

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