Bootstrapping divergence statistics for testing homogeneity in multinomial populations

We consider the problem of testing the equality of ν$\nu$ (ν≥2$\nu \ge 2$) multinomial populations, taking as test statistic a sample version of an f-dissimilarity between the populations, obtained by the replacement of the unknown parameters in the expression of the f-dissimilarity among the theoretical populations, by their maximum likelihood estimators. The null distribution of this test statistic is usually approximated by its limit, the asymptotic null distribution. Here we study another way to approximate it, the bootstrap. We show that the bootstrap yields a consistent distribution estimator. We also study by simulation the finite sample performance of the bootstrap distribution and compare it with the asymptotic 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, in addition, cannot always be exactly computed.