Abstract
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 validity of Edgeworth expansions. Moreover, our proof for the first order also provides us with a result about Edgeworth expansions for smooth functions.
Citation
Walter Schneller. "Edgeworth Expansions for Linear Rank Statistics." Ann. Statist. 17 (3) 1103 - 1123, September, 1989. https://doi.org/10.1214/aos/1176347258
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