Maximally selected chi-square statistics and binary splits of nominal variables - Anne-Laure Boulesteix (Ludwig-Maximilians-Universität München, Sonderforschungsbereich 386 - Statistische Analyse diskreter Strukturen, 2005)
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.
urn:nbn:de:bvb:19-epub-1818-8
Keywords: 519; Categorical variables; association test; contingency table; exact distribution; variable selection; selection bias