Open Access
Translator Disclaimer
oct 2000 Bootstrap relative errors and sub-exponential distributions
Andrew T.A. Wood
Author Affiliations +
Bernoulli 6(5): 809-834 (oct 2000).


For the purposes of this paper, a distribution is sub-exponential if it has finite variance but its moment generating function is infinite on at least one side of the origin. The principal aim here is to study the relative error properties of the bootstrap approximation to the true distribution function of the sample mean in the important sub-exponential cases. Our results provide a fairly general description of how the bootstrap approximation breaks down in the tail when the underlying distribution is sub-exponential and satisfies some very mild additional conditions. The broad conclusion we draw is that the accuracy of the bootstrap approximation in the tail depends, in a rather sensitive way, on the precise tail behaviour of the underlying distribution. Our results are applied to several sub-exponential distributions, including the lognormal. The lognormal case is of particular interest because, as the simulation studies of Lee and Young have shown, bootstrap confidence intervals can have very poor coverage accuracy when applied to data from the lognormal.


Download Citation

Andrew T.A. Wood. "Bootstrap relative errors and sub-exponential distributions." Bernoulli 6 (5) 809 - 834, oct 2000.


Published: oct 2000
First available in Project Euclid: 6 April 2004

zbMATH: 0958.62017
MathSciNet: MR2002A:62067

Keywords: Edgeworth expansion , Moderate deviations , percentile method , tail probability

Rights: Copyright © 2000 Bernoulli Society for Mathematical Statistics and Probability


Vol.6 • No. 5 • oct 2000
Back to Top