Title: Testing the equality of a large number of populations
Authors: Marta Cousido Rocha - University of Vigo (Spain) [presenting]
Maria Dolores Jimenez-Gamero - Universidad de Sevilla (Spain)
Virtudes Alba-Fernandez - University of Jaen (Spain)
Abstract: Given $k$ independent samples with finite but arbitrary dimension, the problem of testing for the equality of their distributions, that can be continuous, discrete or mixed, is considered. In contrast to the classical setting where $k$ is assumed to be fixed, and the sample size from each population increases without bound, $k$ is assumed to be large, and the size of each sample is either bounded or small in comparison to $k$. The asymptotic distribution of the considered test statistic is stated under the null hypothesis of equality of the $k$ distributions, as well as under alternatives, which let us study the consistency of the resulting test. Specifically, it is shown that the proposed test statistic is asymptotically free distributed under the null hypothesis. The finite sample performance of the test based on the asymptotic null distribution is studied via simulation.