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2007 Edgeworth Expansions for a Sample Sum from a Finite Set of Independent Random Variables
Zhishui Hu, John Robinson, Qiying Wang
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Electron. J. Probab. 12: 1402-1417 (2007). DOI: 10.1214/EJP.v12-447

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.

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Zhishui Hu. John Robinson. Qiying Wang. "Edgeworth Expansions for a Sample Sum from a Finite Set of Independent Random Variables." Electron. J. Probab. 12 1402 - 1417, 2007. https://doi.org/10.1214/EJP.v12-447

Information

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

zbMATH: 1127.60020
MathSciNet: MR2354163
Digital Object Identifier: 10.1214/EJP.v12-447

Subjects:
Primary: 60F05 , 60F15
Secondary: 62E20

Keywords: Edgeworth expansion , finite population , sampling without replacement

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