The Annals of Statistics

Asymptotic Iterated Bootstrap Confidence Intervals

Stephen M. S. Lee and G. Alastair Young

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An iterated bootstrap confidence interval requires an additive correction to be made to the nominal coverage level of an uncorrected interval. Such correction is usually performed using a computationally intensive Monte Carlo simulation involving two nested levels of bootstrap sampling. Asymptotic expansions of the required correction and the iterated interval endpoints are used to provide two new computationally efficient methods for constructing an approximation to the iterated bootstrap confidence interval. The first asymptotic interval replaces the need for a second level of bootstrap sampling with a series of preliminary analytic calculations, which are readily automated, and from which an approximation to the coverage correction is easily obtained. The second interval directly approximates the endpoints of the iterated interval and yields, for the first time, the possibility of constructing an approximation to an iterated bootstrap confidence interval which does not require any resampling. The theoretical properties of the two intervals are considered. The computation required for their construction is detailed and has been coded in a fully automatic user-friendly Fortran program which may be obtained by anonymous ftp. A simulation study which illustrates their effectiveness on three examples is presented.

Article information

Ann. Statist., Volume 23, Number 4 (1995), 1301-1330.

First available in Project Euclid: 11 April 2007

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


Primary: 62G09: Resampling methods
Secondary: 62G15: Tolerance and confidence regions 62G20: Asymptotic properties

Asymptotic bootstrap coverage error Edgeworth expansion iterated bootstrap percentile method resampling


Lee, Stephen M. S.; Young, G. Alastair. Asymptotic Iterated Bootstrap Confidence Intervals. Ann. Statist. 23 (1995), no. 4, 1301--1330. doi:10.1214/aos/1176324710.

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