Estimating Rao’s statistic distribution for testing uniform association in cross-classifications

We consider the problem of testing uniform association in cross-classifications with ordered categories taking as test statistic a Rϕ divergence. The asymptotic null distribution of any test statistic in this class is not free because it depends on the unknown true vector of probabilities, so in practice one has to approximate it in order to get an estimate of the null distribution. As an alternative approach we propose to approximate the null distribution of the test statistic by bootstrapping. We show that the bootstrap yields a consistent null distribution estimator. The finite sample performance of the bootstrap estimator is studied by simulation. We also compare it empirically with the asymptotic null approximation. From the simulations it can be concluded that it is worth calculating the bootstrap estimator, because it is more accurate than the approximation yielded by the asymptotic null distribution which, furthermore, cannot always be exactly computed. Finally, the results are applied to some real data sets.