IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v38y1991i1p70-81.html
   My bibliography  Save this article

On the error incurred using the bootstrap variance estimate when constructing confidence intervals for quantiles

Author

Listed:
  • Hall, Peter
  • Martin, Michael A.

Abstract

We show that the coverage error of confidence intervals and level error of hypothesis tests for population quantiles constructed using the bootstrap estimate of sample quantile variance is of precise order n-1/2 in both one- and two-sided cases. This contrasts markedly with more classical problems, where the error is of order n-1/2 in the one-sided case, but n-1 in the two-sided case, and results from an unusual feature of the Edgeworth expansion in that the leading term, of order n-1/2, is proportional to a polynomial containing both odd and even powers of the argument. Our results also show that for two-sided confidence intervals and hypothesis tests, and in large samples, the bootstrap variance estimate is inferior to the Siddiqui-Bloch-Gastwirth variance estimate provided the smoothing parameter in the latter is chosen to minimize coverage/level error.

Suggested Citation

  • Hall, Peter & Martin, Michael A., 1991. "On the error incurred using the bootstrap variance estimate when constructing confidence intervals for quantiles," Journal of Multivariate Analysis, Elsevier, vol. 38(1), pages 70-81, July.
  • Handle: RePEc:eee:jmvana:v:38:y:1991:i:1:p:70-81
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/0047-259X(91)90032-W
    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. Stewart, Mark, 2011. "Quantile estimates of counterfactual distribution shifts and the impact of minimum wage increases on the wage distribution," The Warwick Economics Research Paper Series (TWERPS) 958, University of Warwick, Department of Economics.
    2. Daniel Janas, 1993. "A smoothed bootstrap estimator for a studentized sample quantile," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 45(2), pages 317-329, June.
    3. Donald W.K. Andrews & Moshe Buchinsky, 1997. "On the Number of Bootstrap Repetitions for Bootstrap Standard Errors, Confidence Intervals, and Tests," Cowles Foundation Discussion Papers 1141R, Cowles Foundation for Research in Economics, Yale University.
    4. Arup Bose & Probal Chaudhuri, 1993. "On the dispersion of multivariate median," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 45(3), pages 541-550, September.

    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:38:y:1991:i:1:p:70-81. See general information about how to correct material in RePEc.

    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 bibliographic 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.

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

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.