Edgeworth Expansions for Linear Rank Statistics
线性秩统计量的 Edgeworth 展开
An Edgeworth expansion of first order is established for general linear rank statistics under the null hypothesis with a remainder term that is usually of order $n^{-1}$. Furthermore, corresponding results for the second order are formulated, but not proved here. The proof for the first order is based on Stein's method and on an extension of a combinatorial method of Bolthausen. It is also shown that conditions of van Zwet imply up to a small factor our conditions for the…