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.

给定k个具有有限但任意维度的独立样本，本文讨论了测试其分布是否相等的问题，这些分布可以是连续的，离散的或混合的。与假设k是固定的并且来自每个总体的样本大小无限制地增加的经典设置相反，这里假设k很大，并且与k相比，每个样本的大小要么是有界的，要么是小的。两个检验统计量的渐近分布在k相等的零假设下表示分布以及替代项下的分布，这使我们能够研究所得测试的渐近能力。具体来说，表明在零假设下，两个检验统计量都是渐近自由分布的。通过仿真研究了基于渐近零分布的测试的有限样本性能。包括该建议对真实数据集的应用。讨论了所提出的过程对无限维数据的使用以及其他可能的扩展。