Ӧ�ø���ͳ�� 2009, 25(2) 155-163 DOI:      ISSN: 1001-4268 CN: 31-1256

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Spectral Decomposition Method for the Covariance Matrix of Variance Components Model
Liu Wei,Wang Songgui,Dong Ping
Academy of Mathematics and Systems Science, Chinese Academy of Sciences;College of Applied Sciences, Beijing University of Technology;chool of Mathematical Sciences of GUCAS
Abstract: For the balanced variance components model, the main contribution of this thesis is to provide a new spectral decomposition method for the covariance matrix. The computation of this new method is simple, it can give the number of different eigenvalues of covariance matrix and closed form of the projective matrices corresponding to its eigenvalues. Based on this new method we discuss several properties of variance components model. Further more, this thesis studies general variance components model. Firstly, we give the definition of simple spectral decomposition and obtain a necessary and sufficient condition of existence of simple spectral decomposition, then discuss some characters. To this kind of models, the application in statistical inference of simple spectral decomposition is also discussed.
Keywords: Variance components model   spectral decomposition estimation   maximum likelihood estimation   simple spectral decomposition.  
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