IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v17y1984i1p127-136.html
   My bibliography  Save this article

A strong limit theorem for the oscillation modulus of the uniform empirical quantile process

Author

Listed:
  • Mason, David M.

Abstract

Stute (1982) and Mason, Shorack and Wellner (1983) have recently completed a thorough study of the limiting behavior of the oscillation of the uniform empirical process. In this paper, the corresponding oscillation behavior of the uniform empirical quantile process is investigated. It is shown to be closely related to the limiting behavior of the maximum k-spacing of n independent Uniform (0, 1) random variables, where k can possibly be a function of n. Results of this type are directly applicable to the study of the strong consistency properties of various types of density estimators.

Suggested Citation

  • Mason, David M., 1984. "A strong limit theorem for the oscillation modulus of the uniform empirical quantile process," Stochastic Processes and their Applications, Elsevier, vol. 17(1), pages 127-136, May.
    • Handle: RePEc:eee:spapps:v:17:y:1984:i:1:p:127-136
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/0304-4149(84)90315-6
    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. Philippe Berthet, 1997. "On the Rate of Clustering to the Strassen Set for Increments of the Uniform Empirical Process," Journal of Theoretical Probability, Springer, vol. 10(3), pages 557-579, July.
    2. Paul Deheuvels, 1998. "On the Approximation of Quantile Processes by Kiefer Processes," Journal of Theoretical Probability, Springer, vol. 11(4), pages 997-1018, October.
    3. Paul Deheuvels & Sarah Ouadah, 2013. "Uniform-in-Bandwidth Functional Limit Laws," Journal of Theoretical Probability, Springer, vol. 26(3), pages 697-721, September.
    4. Berthet, Philippe, 2005. "Inner rates of coverage of Strassen type sets by increments of the uniform empirical and quantile processes," Stochastic Processes and their Applications, Elsevier, vol. 115(3), pages 493-537, March.

    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:spapps:v:17:y:1984:i:1:p:127-136. 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/505572/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.