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How close are alternative bootstrap P-values?

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  • Lloyd, Chris J.

Abstract

The parametric bootstrap P-value based on a test statistic T is the exact tail probability of the observed value t, with the null maximum likelihood estimate of the nuisance parameters substituted. This P-value is known to lead to tests whose size is closer to nominal asymptotically than the first order test. One issue that has not been addressed is whether parametric bootstrap might reduce the impact of the choice of basic test statistic. It is shown that bootstrap P-values based on different first order statistics differ to second order i.e to O(m-1) where m is a measure of sample size. Boostrap reduces the impact of the test statistic choice. Just as importantly, it is shown numerically that this asymptotic rate may under-estimate how close alternative bootstrap P-values are for small sample sizes.

Suggested Citation

  • Lloyd, Chris J., 2010. "How close are alternative bootstrap P-values?," Statistics & Probability Letters, Elsevier, vol. 80(23-24), pages 1972-1976, December.
    • Handle: RePEc:eee:stapro:v:80:y:2010:i:23-24:p:1972-1976
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    References listed on IDEAS

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    1. repec:dau:papers:123456789/555 is not listed on IDEAS
    2. A. C. Davison & D. A. S. Fraser & N. Reid, 2006. "Improved likelihood inference for discrete data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(3), pages 495-508, June.
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    4. D.A.S. Fraser & Judith Rousseau, 2008. "Studentization and deriving accurate p-values," Biometrika, Biometrika Trust, vol. 95(1), pages 1-16.
    5. Lee, Stephen M.S. & Young, G. Alastair, 2005. "Parametric bootstrapping with nuisance parameters," Statistics & Probability Letters, Elsevier, vol. 71(2), pages 143-153, February.
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    Cited by:

    1. Lloyd, Chris J., 2012. "Computing highly accurate or exact P-values using importance sampling," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1784-1794.

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