
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 |
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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 |
URN: | urn:nbn:de:bvb:19-epub-1818-8 |
Item ID: | 1818 |
Date Deposited: | 11. Apr 2007 |
Last Modified: | 29. Apr 2016, 08:50 |