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April 1997 An Edgeworth expansion for symmetric statistics
V. Bentkus, F. Götze, W. R. van Zwet
Ann. Statist. 25(2): 851-896 (April 1997). DOI: 10.1214/aos/1031833676

Abstract

We consider asymptotically normal statistics which are symmetric functions of N i.i.d. random variables. For these statistics we prove the validity of an Edgeworth expansion with remainder $O(N^{-1})$ under Cramér's condition on the linear part of the statistic and moment assumptions for all parts of the statistic. By means of a counterexample we show that it is generally not possible to obtain an Edgeworth expansion with remainder $o(N^{-1})$ without imposing additional assumptions on the structure of the nonlinear part of the statistic.

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V. Bentkus. F. Götze. W. R. van Zwet. "An Edgeworth expansion for symmetric statistics." Ann. Statist. 25 (2) 851 - 896, April 1997. https://doi.org/10.1214/aos/1031833676

Information

Published: April 1997
First available in Project Euclid: 12 September 2002

zbMATH: 0920.62016
MathSciNet: MR1439326
Digital Object Identifier: 10.1214/aos/1031833676

Subjects:
Primary: 62E20
Secondary: 60F05

Rights: Copyright © 1997 Institute of Mathematical Statistics

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Vol.25 • No. 2 • April 1997
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