Testing the equality of a large number of populations

Given k independent samples with finite but arbitrary dimension, this paper deals with the problem of testing for the equality of their distributions that can be continuous, discrete or mixed. In contrast to the classical setting where k is assumed to be fixed and the sample size from each population increases without bound, here k is assumed to be large and the size of each sample is either bounded or small in comparison with k. The asymptotic distribution of two test statistics is stated under the null hypothesis of the equality of the k distributions as well as under alternatives, which let us to study the asymptotic power of the resulting tests. Specifically, it is shown that both test statistics are asymptotically free distributed under the null hypothesis. The finite sample performance of the tests based on the asymptotic null distribution is studied via simulation. An application of the proposal to a real data set is included. The use of the proposed procedure for infinite dimensional data, as well as other possible extensions, are discussed.

Automated summary

This paper examines the problem of testing for the equality of distributions of k independent samples with finite but arbitrary dimension, providing the asymptotic distribution of two test statistics under the null hypothesis and under alternatives. Both test statistics are shown to be asymptotically free distributed under the null hypothesis. The finite sample performance of the tests based on the asymptotic null distribution is studied through simulation, with an application to a real data set included.