An Edgeworth Expansion for Simple Linear Rank Statistics under the Null Hypothesis

摘要

Assuming certain restrictions for the values of the regression constants and the scores generating functions, an Edgeworth expansion for simple linear rank statistics is established under the null hypothesis with a remainder function of 1/N for a wide class of score generating functions, including the normal quantile function. The theorem is proved and the results are compared with those in Bickel and VanZwet for the two-sample linear rank statistic.