Maximally selected chi-square statistics and binary splits of nominal variables

Boulesteix, Anne-Laure (2005): Maximally selected chi-square statistics and binary splits of nominal variables. Collaborative Research Center 386, Discussion Paper 449

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 pregnancy and birth data set.

• Item Type: Paper
• Keywords: Categorical variables, association test, contingency table, exact distribution, variable selection, selection bias
• Faculties: Mathematics, Computer Science and Statistics > Statistics > Collaborative Research Center 386; Special Research Fields > Special Research Field 386
• Subjects: 500 Science > 510 Mathematics