IDEAS home Printed from
   My bibliography  Save this article

The Spectral Decomposition of Covariance Matrices for the Variance Components Models


  • Jian-Hong, Shi
  • Song-Gui, Wang


The aim of this paper is to propose a simple method to determine the number of distinct eigenvalues and the spectral decomposition of covariance matrix for a variance components model. The method introduced in this paper is based on a partial ordering of symmetric matrix and relation matrix. A method is also given for checking straightforwardly whether these distinct eigenvalues are linear dependent as functions of variance components. Some examples and applications to illustrate the results are presented.

Suggested Citation

  • Jian-Hong, Shi & Song-Gui, Wang, 2006. "The Spectral Decomposition of Covariance Matrices for the Variance Components Models," Journal of Multivariate Analysis, Elsevier, vol. 97(10), pages 2190-2205, November.
  • Handle: RePEc:eee:jmvana:v:97:y:2006:i:10:p:2190-2205

    Download full text from publisher

    File URL:
    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.

    References listed on IDEAS

    1. Nerlove, Marc, 1971. "A Note on Error Components Models," Econometrica, Econometric Society, vol. 39(2), pages 383-396, March.
    2. Balestra, Pietro, 1973. "Best quadratic unbiased estimators of the variance-covariance matrix in normal regression," Journal of Econometrics, Elsevier, vol. 1(1), pages 17-28, March.
    3. Fuller, Wayne A. & Battese, George E., 1974. "Estimation of linear models with crossed-error structure," Journal of Econometrics, Elsevier, vol. 2(1), pages 67-78, May.
    Full references (including those not matched with items on IDEAS)


    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:97:y:2006:i:10:p:2190-2205. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu). General contact details of provider: .

    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.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with 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.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.