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December, 1986 On the Number of Bootstrap Simulations Required to Construct a Confidence Interval
Peter Hall
Ann. Statist. 14(4): 1453-1462 (December, 1986). DOI: 10.1214/aos/1176350169


We make two points about the number, $B$ of bootstrap simulations needed to construct a percentile-$t$ confidence interval based on an $n$ sample from a continuous distribution: (i) The bootstrap's reduction of error of coverage probability, from $O(n^{-1/2})$ to $O(n^{-1})$, is available uniformly in $B$, provided nominal coverage probability is a multiple of $(B + 1)^{-1}$. In fact, this improvement is available even if the number of simulations is held fixed as $n$ increases. However, smaller values of $B$ can result in longer confidence intervals. (ii) In a large sample, the simulated statistic values behave like random observations from a continuous distribution, unless $B$ increases faster than any power of sample size. Only if $B$ increases exponentially quickly with $n$ is there a detectable effect due to discreteness of the bootstrap statistic.


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Peter Hall. "On the Number of Bootstrap Simulations Required to Construct a Confidence Interval." Ann. Statist. 14 (4) 1453 - 1462, December, 1986.


Published: December, 1986
First available in Project Euclid: 12 April 2007

zbMATH: 0611.62048
MathSciNet: MR868311
Digital Object Identifier: 10.1214/aos/1176350169

Primary: 62G15
Secondary: 62E20

Rights: Copyright © 1986 Institute of Mathematical Statistics


Vol.14 • No. 4 • December, 1986
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