Open Access
Translator Disclaimer
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


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.


Download Citation

V. Bentkus. F. Götze. W. R. van Zwet. "An Edgeworth expansion for symmetric statistics." Ann. Statist. 25 (2) 851 - 896, April 1997.


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

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

Primary: 62E20
Secondary: 60F05

Keywords: $U$-statistics , asymptotic expansion , Edgeworth expansions , functionals of empirical distribution functions , functions of sample means , Hoeffdings's decomposition , linear combinations of order statistics , Student's statistic , symmetric statistics

Rights: Copyright © 1997 Institute of Mathematical Statistics


Vol.25 • No. 2 • April 1997
Back to Top