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On the relative performance of bootstrap and Edgeworth approximations of a distribution function


  • Hall, Peter


Performance of the bootstrap for estimating tail probabilities is usually explained by saying that the bootstrap provides a one-term Edgeworth correction. However, simulation studies show that the bootstrap usually performs better than explicit Edgeworth correction. We present a theory which explains this empirical observation. The theory is based on a comparison of relative error in bootstrap and Edgeworth approximation formulae and uses expansions of large deviation probabilities. We treat general Edgeworth approximations, not simply the one-term corrections usually associated with the bootstrap. We show that bootstrap and Edgeworth approximations are equivalent out to a certain distance in the tail. Beyond that point the bootstrap performs markedly better than Edgeworth correction, except for the case of extreme tail probabilities where it is possible for bootstrap and Edgeworth approximations to outperform one another, depending on the sign of skewness. In the case of one-term Edgeworth correction the bootstrap performs markedly better for both moderate and large deviations, except in the extreme tails. Even there the bootstrap outperforms Edgeworth correction if skewness is of the right sign.

Suggested Citation

  • Hall, Peter, 1990. "On the relative performance of bootstrap and Edgeworth approximations of a distribution function," Journal of Multivariate Analysis, Elsevier, vol. 35(1), pages 108-129, October.
  • Handle: RePEc:eee:jmvana:v:35:y:1990:i:1:p:108-129

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    Cited by:

    1. Andrea Pallini, 2000. "Efficient bootstrap estimation of distribution functions," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(1-2), pages 81-95.
    2. Dalla, Violetta & Hidalgo, Javier, 2005. "A parametric bootstrap test for cycles," LSE Research Online Documents on Economics 6829, London School of Economics and Political Science, LSE Library.
    3. Dalla, Violetta & Hidalgo, Javier, 2005. "A parametric bootstrap test for cycles," Journal of Econometrics, Elsevier, vol. 129(1-2), pages 219-261.
    4. Borovskikh, Yuri V. & Robinson, John, 2008. "Large deviations of bootstrapped U -statistics," Journal of Multivariate Analysis, Elsevier, vol. 99(8), pages 1793-1806, September.
    5. Violetta Dalla & Javier Hidalgo, 2005. "A Parametric Bootstrap Test for Cycles," STICERD - Econometrics Paper Series 486, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.


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