Electronic Journal of Probability

Edgeworth Expansions for a Sample Sum from a Finite Set of Independent Random Variables

Zhishui Hu, John Robinson, and Qiying Wang

Full-text: Open access

Abstract

Let $\{X_1,\cdots ,X_N\}$ be a set of $N$ independent random variables, and let $S_n$ be a sum of $n$ random variables chosen without replacement from the set $\{X_1, \cdots , X_N\}$ with equal probabilities. In this paper we give a one-term Edgeworth expansion of the remainder term for the normal approximation of $S_n$ under mild conditions.

Article information

Source
Electron. J. Probab., Volume 12 (2007), paper no. 52, 1402-1417.

Dates
Accepted: 4 November 2007
First available in Project Euclid: 1 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1464818523

Digital Object Identifier
doi:10.1214/EJP.v12-447

Mathematical Reviews number (MathSciNet)
MR2354163

Zentralblatt MATH identifier
1127.60020

Subjects
Primary: 60F05: Central limit and other weak theorems 60F15: Strong theorems
Secondary: 62E20: Asymptotic distribution theory

Keywords
Edgeworth expansion finite population sampling without replacement

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

Hu, Zhishui; Robinson, John; Wang, Qiying. Edgeworth Expansions for a Sample Sum from a Finite Set of Independent Random Variables. Electron. J. Probab. 12 (2007), paper no. 52, 1402--1417. doi:10.1214/EJP.v12-447. https://projecteuclid.org/euclid.ejp/1464818523


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