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September, 1988 Theoretical Comparison of Bootstrap Confidence Intervals
Peter Hall
Ann. Statist. 16(3): 927-953 (September, 1988). DOI: 10.1214/aos/1176350933


We develop a unified framework within which many commonly used bootstrap critical points and confidence intervals may be discussed and compared. In all, seven different bootstrap methods are examined, each being usable in both parametric and nonparametric contexts. Emphasis is on the way in which the methods cope with first- and second-order departures from normality. Percentile-$t$ and accelerated bias-correction emerge as the most promising of existing techniques. Certain other methods are shown to lead to serious errors in coverage and position of critical point. An alternative approach, based on "shortest" bootstrap confidence intervals, is developed. We also make several more technical contributions. In particular, we confirm Efron's conjecture that accelerated bias-correction is second-order correct in a variety of multivariate circumstances, and give a simple interpretation of the acceleration constant.


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Peter Hall. "Theoretical Comparison of Bootstrap Confidence Intervals." Ann. Statist. 16 (3) 927 - 953, September, 1988.


Published: September, 1988
First available in Project Euclid: 12 April 2007

MathSciNet: MR959185
zbMATH: 0663.62046
Digital Object Identifier: 10.1214/aos/1176350933

Primary: 62F25
Secondary: 62E20, 62G15

Rights: Copyright © 1988 Institute of Mathematical Statistics


Vol.16 • No. 3 • September, 1988
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