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- W2064989810 abstract "In this paper we develop a method for obtaining estimators of the correlation matrices from k groups when these correlation matrices have the same set of eigenvectors. These estimators are obtained by utilizing the spectral decomposition of a symmetric matrix; that is, we obtain an estimate, say P̂, of the matrix P containing the common normalized eigenvectors along with estimates of the eigenvalues for each of the k correlation matrices. It is shown that the rank of the Hadamard product, P̂ P̂, is a crucial factor in the estimation of these correlation matrices. Consequently, our procedure begins with an initial estimate of P which is then used to obtain an estimate P̂ such that P̂ ⊙ P̂ has its rank less than or equal to some specified value. Initial estimators of the eigenvalues of Ωi, the correlation matrix for the ith group, are then used to obtain refined estimators which, when put in the diagonal matrix D̂i as its diagonal elements, are such that P̂D̂iP̂′ has correlation-matrix structure." @default.
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- W2064989810 date "1998-06-01" @default.
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- W2064989810 title "Estimating correlation matrices that have common eigenvectors" @default.
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- W2064989810 doi "https://doi.org/10.1016/s0167-9473(98)00027-9" @default.
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