IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v35y1990i1p108-129.html
   My bibliography  Save this article

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

Author

Listed:
  • Hall, Peter

Abstract

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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/0047-259X(90)90019-E
    Download Restriction: Full text for ScienceDirect subscribers only

    As the access to this document is restricted, you may want to search for a different version of it.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:jmvana:v:35:y:1990:i:1:p:108-129. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.