Permutation tests for homogeneity based on the empirical characteristic function

Abstract

In this paper, omnibus tests are proposed for testing the homogeneity of two populations. The tests are based on weighted integrals involving the empirical characteristic function. The consistency of the tests as well as their asymptotic distribution under the null hypothesis are investigated. As the decay of the weight functions tends to infinity, the test statistics approach limit values which are related to moment differences between the two populations. The test procedure is based on resampling from the permutation distribution of the test statistic. The new tests are compared with other omnibus tests for homogeneity via a Monte Carlo procedure.

Keywords:

• Two-sample problem
• Empirical characteristic function
• Nonparametric test