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The Spectral Decomposition of Covariance Matrices for the Variance Components Models

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  • Jian-Hong, Shi
  • Song-Gui, Wang

Abstract

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
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Nerlove, Marc, 1971. "A Note on Error Components Models," Econometrica, Econometric Society, vol. 39(2), pages 383-396, March.
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