IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v208y2025ics0047259x24001052.html
   My bibliography  Save this article

Asymptotics for non-degenerate multivariate U-statistics with estimated nuisance parameters under the null and local alternative hypotheses

Author

Listed:
  • Desgagné, Alain
  • Genest, Christian
  • Ouimet, Frédéric

Abstract

The large-sample behavior of non-degenerate multivariate U-statistics of arbitrary degree is investigated under the assumption that their kernel depends on parameters that can be estimated consistently. Mild regularity conditions are provided which guarantee that once properly normalized, such statistics are asymptotically multivariate Gaussian both under the null hypothesis and sequences of local alternatives. The work of Randles (1982, Ann. Statist.) is extended in three ways: the data and the kernel values can be multivariate rather than univariate, the limiting behavior under local alternatives is studied for the first time, and the effect of knowing some of the nuisance parameters is quantified. These results can be applied to a broad range of goodness-of-fit testing contexts, as shown in two specific examples.

Suggested Citation

  • Desgagné, Alain & Genest, Christian & Ouimet, Frédéric, 2025. "Asymptotics for non-degenerate multivariate U-statistics with estimated nuisance parameters under the null and local alternative hypotheses," Journal of Multivariate Analysis, Elsevier, vol. 208(C).
    • Handle: RePEc:eee:jmvana:v:208:y:2025:i:c:s0047259x24001052
    DOI: 10.1016/j.jmva.2024.105398
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X24001052
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2024.105398?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

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

    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:208:y:2025:i:c:s0047259x24001052. 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.