Exact Null Distributions and Asymptotic Expansions for Rank Test Statistics

摘要

Efficient algorithms are developed for inverting the probability generating functions of the distributions of rank test statistics. A method is given for deriving probability generating functions in a form suitable for inversion. Cases treated include one and two sample linear rank statistics and the Kolmogorov-Smirnov test statistics. A proof is given that one term of the Edgeworth series provides a valid asymptotic expansion for the Wilcoxon two sample distribution. Explicit bounds are given for the error in approximating the distribution by the one term expansion. It is shown that the error in the uncorrected normal approximation is of the order max(1/n, 1/m). (Author)