Estimating correlation matrices that have common eigenvectors
Abbreviated Journal Title
Comput. Stat. Data Anal.
common principal components; Hadamard product; principal components; analysis; PRINCIPAL COMPONENT SUBSPACES; ALGORITHM; TESTS; Computer Science, Interdisciplinary Applications; Statistics &; Probability
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 (P) over cap 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, (P) over cap.(P) over cap 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 (P) over cap such that (P) over cap.(P) over cap has its rank less than or equal to some specified value. Initial estimators of the eigenvalues of Omega(i), the correlation matrix for the ith group, are then used to obtain refined estimators which, when put in the diagonal matrix (D) over cap(i) as its diagonal elements, are such that (P) over cap (D) over cap(i)(P) over cap has correlation-matrix structure. (C) 1998 Elsevier Science B.V. All rights reserved.
Computational Statistics & Data Analysis
"Estimating correlation matrices that have common eigenvectors" (1998). Faculty Bibliography 1990s. 2442.