IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v7y1977i4p594-597.html
   My bibliography  Save this article

A uniform bound for the deviation of empirical distribution functions

Author

Listed:
  • Devroye, Luc P.

Abstract

If X1, ..., Xn are independent Rd-valued random vectors with common distribution function F, and if Fn is the empirical distribution function for X1, ..., Xn, then, among other things, it is shown that P{supx | Fn(x) | [greater-or-equal, slanted] [epsilon]} [less-than-or-equals, slant] 2e2(2n)de-2n[epsilon]2 for all n[epsilon]2 >= d2. The inequality remains valid if the Xi are not identically distributed and F(x) is replaced by [Sigma]iP{Xi

Suggested Citation

  • Devroye, Luc P., 1977. "A uniform bound for the deviation of empirical distribution functions," Journal of Multivariate Analysis, Elsevier, vol. 7(4), pages 594-597, December.
    • Handle: RePEc:eee:jmvana:v:7:y:1977:i:4:p:594-597
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/0047-259X(77)90071-9
    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. Naaman, Michael, 2021. "On the tight constant in the multivariate Dvoretzky–Kiefer–Wolfowitz inequality," Statistics & Probability Letters, Elsevier, vol. 173(C).
    2. Amiri, Aboubacar & Crambes, Christophe & Thiam, Baba, 2014. "Recursive estimation of nonparametric regression with functional covariate," Computational Statistics & Data Analysis, Elsevier, vol. 69(C), pages 154-172.

    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:7:y:1977:i:4:p:594-597. 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.