The Spectral Decomposition of Covariance Matrices for the Variance Components Models
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.Download Info
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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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Related research
Keywords: Spectral decomposition Variance component Partial ordering;References
References listed on IDEASPlease report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- 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.
- 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.
- Nerlove, Marc, 1971. "A Note on Error Components Models," Econometrica, Econometric Society, vol. 39(2), pages 383-96, March.
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