Divergence statistics for testing uniform association in cross-classifications

In this paper, we consider the problem of testing uniform association in cross-classifications having ordered categories, taking as test statistic one in the family proposed by Conde and Salicrú [J. Conde, M. Salicrú, Uniform association in contingency tables associated to Csiszár divergence, Statistics and Probability Letters 37 (1998) 149–154]. We consider two approximations to the null distribution of the test statistics in this family: an estimation of the asymptotic null distribution and a bootstrap estimator. We prove that both approximations are asymptotically equivalent. To study their finite sample performance, we carried out two simulation experiments, whose results are presented. From the simulations it can be concluded that the bootstrap estimator behaves much better than the estimated asymptotic null distribution.