Two classes of divergence statistics for testing uniform association

Abstract

The problem of testing uniform association in cross-classifications having ordered categories is considered. Two families of test statistics, both based on divergences between certain functions of the observed data, are studied and compared. Our theoretical study is based on asymptotic properties. For each family, two consistent approximations to the null distribution of the test statistic are studied: the asymptotic null distribution and a bootstrap estimator; all the tests considered are consistent against fixed alternatives; finally, we do a local power study. Surprisingly, both families detect the same local alternatives. The finite sample performance of the tests in these two classes is numerically investigated through some simulation experiments. In the light of the obtained results, some practical recommendations are given.

Keywords:

• contingency table
• uniform association
• bootstrap
• consistency
• power

Acknowledgements

The authors thank the anonymous referees for their constructive comments and suggestions which helped to improve the presentation. The research in this paper has been partially supported by grant MTM2008-00018 (Ministerio de Ciencia e Innovación, Spain).