The Annals of Statistics

Uniform Coverage Bounds for Confidence Intervals and Berry-Esseen Theorems for Edgeworth Expansion

Peter Hall and Bing-Yi Jing

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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.

Article information

Source
Ann. Statist. Volume 23, Number 2 (1995), 363-375.

Dates
First available in Project Euclid: 11 April 2007

Permanent link to this document
http://projecteuclid.org/euclid.aos/1176324525

JSTOR
links.jstor.org

Digital Object Identifier
doi:10.1214/aos/1176324525

Mathematical Reviews number (MathSciNet)
MR1332571

Zentralblatt MATH identifier
0824.62043

Subjects
Primary: 62G15: Tolerance and confidence regions
Secondary: 62E20: Asymptotic distribution theory

Keywords
Berry-Esseen bound bootstrap confidence interval coverage error Edgeworth expansion minimax bound skewness

Citation

Hall, Peter; Jing, Bing-Yi. Uniform Coverage Bounds for Confidence Intervals and Berry-Esseen Theorems for Edgeworth Expansion. Ann. Statist. 23 (1995), no. 2, 363--375. doi:10.1214/aos/1176324525. http://projecteuclid.org/euclid.aos/1176324525.


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