A Rank Statistic for Non-parametric k -sample and Change Point Problems

We consider k-sample and change point problems for independent data in a unified way. We propose a test statistic based on the rank statisitcs. The asymptotic distribution under the null hypothesis is shown to be the supremum of the 2-dimensional standard Brownian pillow. Also, the test is shown to be consistent under the alternative that k distribution functions are linearly independent. It is important from practical point of view that our test is not only asymptotically distribution free but also distribution free even for fixed finite sample.