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On a class of m out of n bootstrap confidence intervals

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  • S. M. S. Lee

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.

Suggested Citation

  • S. M. S. Lee, 1999. "On a class of m out of n bootstrap confidence intervals," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(4), pages 901-911.
    • Handle: RePEc:bla:jorssb:v:61:y:1999:i:4:p:901-911
    DOI: 10.1111/1467-9868.00209
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    Cited by:

    1. Freitag, Gudrun & Munk, Axel, 2005. "On Hadamard differentiability in k-sample semiparametric models--with applications to the assessment of structural relationships," Journal of Multivariate Analysis, Elsevier, vol. 94(1), pages 123-158, May.

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