Berry-Esseen Theorems for Simple Linear Rank Statistics Under the Null- Hypothesis

Berry-Esseen bounds of order $O(N^{-1/2})$ are established for simple linear rank statistics under the null-hypothesis. The theorems are proved for a wide class of scores generating functions which include the normal quantile function. This improves earlier results under the null-hypothesis in von Bahr (1976), Huskova (1977, 1979) and Ho and Chen (1978).