IDEAS home Printed from https://ideas.repec.org/a/oup/biomet/v110y2023i3p777-797..html
   My bibliography  Save this article

High-dimensional analysis of variance in multivariate linear regression

Author

Listed:
  • Zhipeng Lou
  • Xianyang Zhang
  • Wei Biao Wu

Abstract

SummaryIn this paper, we develop a systematic theory for high-dimensional analysis of variance in multivariate linear regression, where the dimension and the number of coefficients can both grow with the sample size. We propose a new U-type statistic to test linear hypotheses and establish a high-dimensional Gaussian approximation result under fairly mild moment assumptions. Our general framework and theory can be used to deal with the classical one-way multivariate analysis of variance, and the nonparametric one-way multivariate analysis of variance in high dimensions. To implement the test procedure, we introduce a sample-splitting-based estimator of the second moment of the error covariance and discuss its properties. A simulation study shows that our proposed test outperforms some existing tests in various settings.

Suggested Citation

  • Zhipeng Lou & Xianyang Zhang & Wei Biao Wu, 2023. "High-dimensional analysis of variance in multivariate linear regression," Biometrika, Biometrika Trust, vol. 110(3), pages 777-797.
    • Handle: RePEc:oup:biomet:v:110:y:2023:i:3:p:777-797.
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1093/biomet/asad001
    Download Restriction: Access to full text is restricted to subscribers.
    ---><---

    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:oup:biomet:v:110:y:2023:i:3:p:777-797.. 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: Oxford University Press (email available below). General contact details of provider: https://academic.oup.com/biomet .

    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.