Burbea–Rao divergence based statistics for testing uniform association

Two families of tests for testing uniform association in cross-classification having ordered categories are considered. The test statistics of the tests in these two families are based on Burbea–Rao divergences between certain functions of the observed data. The objective of this paper is to compare these families. The comparison is done both theoretically and numerically. The theoretical study is based on asymptotic properties. For each family, two consistent approximations to the null distribution of the test statistic are studied: an estimation of the asymptotic null distribution and a bootstrap estimator. The power against fixed and local alternatives is also studied. Surprisingly, although the way in which each family measures deviations from the null hypothesis is rather different, the large sample power properties of these two families are quite similar, since both families are able to detect the same set of local alternatives. So, they should be compared for finite sample sizes. This task is numerically investigated through some simulation experiments.