Open Access
September, 1989 Edgeworth Expansions for Linear Rank Statistics
Walter Schneller
Ann. Statist. 17(3): 1103-1123 (September, 1989). DOI: 10.1214/aos/1176347258

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

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Walter Schneller. "Edgeworth Expansions for Linear Rank Statistics." Ann. Statist. 17 (3) 1103 - 1123, September, 1989. https://doi.org/10.1214/aos/1176347258

Information

Published: September, 1989
First available in Project Euclid: 12 April 2007

zbMATH: 0689.62016
MathSciNet: MR1015140
Digital Object Identifier: 10.1214/aos/1176347258

Subjects:
Primary: 60F05
Secondary: 62E20

Keywords: Edgeworth expansion , Linear rank statistic , Stein's method

Rights: Copyright © 1989 Institute of Mathematical Statistics

Vol.17 • No. 3 • September, 1989
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