IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v185y2023ics0167947323000907.html
   My bibliography  Save this article

Hypothesis testing on compound symmetric structure of high-dimensional covariance matrix

Author

Listed:
  • Zhao, Kaige
  • Zou, Tingting
  • Zheng, Shurong
  • Chen, Jing

Abstract

Testing the population covariance matrix is an important topic in multivariate statistical analysis. Owing to the difficulty of establishing the central limit theorem for the test statistic based on sample covariance matrix, in most of the existing literature, it is assumed that the population covariance matrix is bounded in spectral norm as the dimension tends to infinity. Four test statistics are proposed for testing the compound symmetric structure of the population covariance matrix, which has an unbounded spectral norm as the dimension tends to infinity. Three of these tests maintain high power against different kinds of dense alternatives. The asymptotic properties of these statistics are constructed under the null hypothesis and a specific alternative hypothesis. Moreover, extensive simulation studies and an analysis of real data are conducted to evaluate the performance of our proposed tests. The simulation results show that the proposed tests outperform existing methods.

Suggested Citation

  • Zhao, Kaige & Zou, Tingting & Zheng, Shurong & Chen, Jing, 2023. "Hypothesis testing on compound symmetric structure of high-dimensional covariance matrix," Computational Statistics & Data Analysis, Elsevier, vol. 185(C).
    • Handle: RePEc:eee:csdana:v:185:y:2023:i:c:s0167947323000907
    DOI: 10.1016/j.csda.2023.107779
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947323000907
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2023.107779?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:csdana:v:185:y:2023:i:c:s0167947323000907. 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/locate/csda .

    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.