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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
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    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.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 97 (2006)
    Issue (Month): 10 (November)
    Pages: 2190-2205

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    Handle: RePEc:eee:jmvana:v:97:y:2006:i:10:p:2190-2205

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    Related research

    Keywords: Spectral decomposition Variance component Partial ordering;

    References

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    1. 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.
    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. Nerlove, Marc, 1971. "A Note on Error Components Models," Econometrica, Econometric Society, vol. 39(2), pages 383-96, March.
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