## The Annals of Statistics

### Edgeworth Expansion of a Function of Sample Means

#### Abstract

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.

#### Article information

Source
Ann. Statist., Volume 19, Number 3 (1991), 1295-1315.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176348250

Digital Object Identifier
doi:10.1214/aos/1176348250

Mathematical Reviews number (MathSciNet)
MR1126326

Zentralblatt MATH identifier
0741.62016

JSTOR
links.jstor.org

Subjects
Primary: 60F05: Central limit and other weak theorems
Secondary: 62E20: Asymptotic distribution theory

#### Citation

Bai, Z. D.; Rao, C. Radhakrishna. Edgeworth Expansion of a Function of Sample Means. Ann. Statist. 19 (1991), no. 3, 1295--1315. doi:10.1214/aos/1176348250. https://projecteuclid.org/euclid.aos/1176348250