Limit theorems for rank statistics

The purpose of the paper is to extend the weak asymptotic results for the weighted partial sums of i.i.d. random variables to the weighted partial sums of rank scores. These results then suggest various test procedures for the change point problem. The crucial tools in the proofs are martingale property of a class of two-sample rank statistics and the Hájek results (1961) of the simple linear rank statistics.