Open Access
September, 1991 Edgeworth Expansion of a Function of Sample Means
Z. D. Bai, C. Radhakrishna Rao
Ann. Statist. 19(3): 1295-1315 (September, 1991). DOI: 10.1214/aos/1176348250


Many important statistics can be written as functions of sample means of vector variables. A fundamental contribution to the Edgeworth expansion for functions of sample means was made by Bhattacharya and Ghosh. In their work the crucial Cramer $c$-condition is assumed on the joint distribution of all the components of the vector variable. However, in many practical situations, only one or a few of the components satisfy (conditionally) this condition while the rest do not (such a case is referred to as satisfying the partial Cramer $c$-condition). The purpose of this paper is to establish Edgeworth expansions for functions of sample means when only the partial Cramer $c$-condition is satisfied.


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Z. D. Bai. C. Radhakrishna Rao. "Edgeworth Expansion of a Function of Sample Means." Ann. Statist. 19 (3) 1295 - 1315, September, 1991.


Published: September, 1991
First available in Project Euclid: 12 April 2007

zbMATH: 0741.62016
MathSciNet: MR1126326
Digital Object Identifier: 10.1214/aos/1176348250

Primary: 60F05
Secondary: 62E20

Keywords: asymptotic expansion , central limit theorems , Cramer-Edgeworth expansion , function of sample means

Rights: Copyright © 1991 Institute of Mathematical Statistics

Vol.19 • No. 3 • September, 1991
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