Tests for the multivariate k-sample problem based on the empirical characteristic function

Tests for the multivariate k-sample problem are considered. The tests are based on the weighted L2 distance between empirical characteristic functions, and afford an interesting interpretation in terms of a corresponding test statistic based on the L2 distance of pairs of non-parametric density estimators. Depending on the choice of weighting, a corresponding Dirac-type weight function reduces the test to a normalised version of the L2 distance between the sample means of the k populations. Theoretical and computational issues are considered, while the finite-sample implementation based on the permutation distribution of the test statistic shows that the new test performs well in comparison with alternative procedures of the change-point type.