Optimal tests for the general two-sample problem

In this paper we consider the classical problem of testing whether two samples of observations are From the same distribution. Since in many situations the data are multivariate or even of functional type, classical methodology is not applicable. In our approach we conceive a difference in distribution as thr occurrence of a change-point problem, where the change-point is known in advance. This point of view enables us to construct new tests which ale distribution-free under the null hypothesis for general sample spaces, The power Function of the tests is studied under local and global alternatives. Finally some optimality results are provided. (C) 2000 Academic Press AMS 1991 subject classifications: primary 62G05. 62G10, 62G20; secondary 60F05.