Testing homoscedasticity of a large number of populations

Abstract

Given k populations and assuming that independent samples are available from each of them, the problem of testing for the equality of the k population variances is addressed. 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 small in comparison to k. A new test is proposed. The asymptotic distribution of the test statistic is stated under the null hypothesis of equality of the k variances 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. Two bootstrap approximations to the null distribution of the test statistic are also investigated. The finite sample performance of the test based on the asymptotic null distribution and on the two bootstrap approximations, is studied via simulation. The proposal is applied to a real data set.