The k-sample problem using Gini covariance for large k

Given $k$ populations and assuming that independent samples are available from each of them, the problem of testing for the equality of the $k$ populations is addressed. With this aim, an unbiased estimator of the Gini covariance is taken as test statistic. In contrast to the classical setting, where $k$ is kept fixed and the sample size from each population increases without bound, here $k$ is assumed to be large and the size of each sample can either remain bounded or increase with $k$. The asymptotic distribution of the test statistic is stated under the null hypothesis as well as under alternatives, which allows us to study the consistency of the test. Specifically, it is shown that the test statistic is asymptotically free distributed under the null hypothesis. The finite sample performance of the test based on the asymptotic null distribution and the comparison with existing tests are studied via simulation. The proposal is applied to a real data set.