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April, 1995 Uniform Coverage Bounds for Confidence Intervals and Berry-Esseen Theorems for Edgeworth Expansion
Peter Hall, Bing-Yi Jing
Ann. Statist. 23(2): 363-375 (April, 1995). DOI: 10.1214/aos/1176324525

Abstract

We derive upper bounds for the coverage error of confidence intervals for a population mean uniformly over large classes of populations and different types of confidence intervals. It is shown that the order of these bounds is achieved by the normal approximation method for constructing confidence intervals, uniformly over distributions with finite third moment, and, by an empirical Edgeworth correction of this approach, uniformly over smooth distributions with finite fourth moments. These results have straightforward extensions to higher orders of Edgeworth correction and higher orders of moments. Our upper bounds to coverage accuracy are based on Berry-Esseen theorems for Edgeworth expansions of the distribution of the Studentized mean.

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Peter Hall. Bing-Yi Jing. "Uniform Coverage Bounds for Confidence Intervals and Berry-Esseen Theorems for Edgeworth Expansion." Ann. Statist. 23 (2) 363 - 375, April, 1995. https://doi.org/10.1214/aos/1176324525

Information

Published: April, 1995
First available in Project Euclid: 11 April 2007

zbMATH: 0824.62043
MathSciNet: MR1332571
Digital Object Identifier: 10.1214/aos/1176324525

Subjects:
Primary: 62G15
Secondary: 62E20

Rights: Copyright © 1995 Institute of Mathematical Statistics

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Vol.23 • No. 2 • April, 1995
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