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Biometrika 1988 75(4):661-671; doi:10.1093/biomet/75.4.661
© 1988 by Biometrika Trust
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On bootstrap resampling and iteration

PETER HALL and MICHAEL A. MARTIN

Department of Statistics, Australian National University Canberra, A.C.T. 2601, Australia

We propose a single unifying approach to bootstrap resampling, applicable to a very wide range of statistical problems. It enables attention to be focused sharply on one or more characteristics which are of major importance in any particular problem, such as coverage error or length for confidence intervals, or bias for point estimation. Our approach leads easily and directly to a very general form of bootstrap iteration, unifying and generalizing present disparate accounts of this subject. It also provides simple solutions to relatively complex problems, such as a suggestion by Lehmann (1986) for ‘conditionally’ short confidence intervals.

Key Words: Bias reduction • Bootstrap • Confidence interval • Coverage error • Iterated bootstrap • Jackknife • Resampling • Shrinkage


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