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October 1999 A Berry-Esseen Bound for Finite Population Student’s Statistic
M. Bloznelis
Ann. Probab. 27(4): 2089-2108 (October 1999). DOI: 10.1214/aop/1022874830

Abstract

A general and precise Berry –Esseen bound is proved for the Studentized mean based on $N$ random observations drawn without replacement from a finite population. The bound yields the optimal rate $O(N^ -1 /2)$ under minimal conditions. If the Erdős–Rényi condition holds this bound implies the asymptotic normality of Student’s statistic and the self-normalized sum.

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M. Bloznelis. "A Berry-Esseen Bound for Finite Population Student’s Statistic." Ann. Probab. 27 (4) 2089 - 2108, October 1999. https://doi.org/10.1214/aop/1022874830

Information

Published: October 1999
First available in Project Euclid: 31 May 2002

zbMATH: 0984.62010
MathSciNet: MR1742903
Digital Object Identifier: 10.1214/aop/1022874830

Subjects:
Primary: 62E20
Secondary: 60F05

Rights: Copyright © 1999 Institute of Mathematical Statistics

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Vol.27 • No. 4 • October 1999
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