Open Access
December, 1991 Normalizing Transformatins and Bootstrap Confidence Intervals
Sadanori Konishi
Ann. Statist. 19(4): 2209-2225 (December, 1991). DOI: 10.1214/aos/1176348393


This paper considers the problem of constructing approximate confidence intervals for functional parameters in the nonparametric case. The approach based on transformation theory is applied to improve standard confidence intervals. The accelerated bias-corrected percentile interval introduced by Efron relies on the existence of a normalizing transformation with bias and skewness corrections, although calculation does not require explicit knowledge of its functional form. We formally construct such a transformation and estimate bias and skewness correction factors for nonparametric situations. The resulting interval is shown to be second-order accurate. To this end Edgeworth expansions for the distributions of transformed statistics are derived, using the von Mises expansion.


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Sadanori Konishi. "Normalizing Transformatins and Bootstrap Confidence Intervals." Ann. Statist. 19 (4) 2209 - 2225, December, 1991.


Published: December, 1991
First available in Project Euclid: 12 April 2007

zbMATH: 0745.62040
MathSciNet: MR1135171
Digital Object Identifier: 10.1214/aos/1176348393

Primary: 62E20
Secondary: 62G15

Keywords: bootstrap confidence intervals , Edgeworth expansions , statistical functional , transformations , von Mises expansion

Rights: Copyright © 1991 Institute of Mathematical Statistics

Vol.19 • No. 4 • December, 1991
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