On a class of m out of n bootstrap confidence intervals

S. M. S. Lee

Journal of the Royal Statistical Society Series B, 1999, vol. 61, issue 4, 901-911

Abstract: It is widely known that bootstrap failure can often be remedied by using a technique known as the ‘m out of n’ bootstrap, by which a smaller number, m say, of observations are resampled from the original sample of size n. In successful cases of the bootstrap, the m out of n bootstrap is often deemed unnecessary. We show that the problem of constructing nonparametric confidence intervals is an exceptional case. By considering a new class of m out of n bootstrap confidence limits, we develop a computationally efficient approach based on the double bootstrap to construct the optimal m out of n bootstrap intervals. We show that the optimal intervals have a coverage accuracy which is comparable with that of the classical double‐bootstrap intervals, and we conduct a simulation study to examine their performance. The results are in general very encouraging. Alternative approaches which yield even higher order accuracy are also discussed.

Date: 1999
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