A test for the two-sample problem based on empirical characteristic functions

A class of tests for the two sample problem that is based on the empirical characteristic function is investigated. They can be applied to continuous as well as to discrete data of any arbitrary fixed dimension. The tests are consistent against any fixed alternatives for adequate choices of the weight function involved in the definition of the test statistic. Both the bootstrap and the permutation procedures can be employed to estimate consistently the null distribution. The goodness of these approximations and the power of some tests in this class for finite sample sizes are investigated by simulation.