Estimating correlation matrices that have common eigenvectors

✍ Scribed by James R Schott

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 853 KB
• Volume: 27
• Category: Article
• ISSN: 0167-9473
• DOI: 10.1016/s0167-9473(98)00027-9

✦ Synopsis

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, 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,/5 Q/5, 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/5 such that/5 ®/5 has its rank less than or equal to some specified value. Initial estimators of the eigenvalues of I2i, the correlation matrix for the ith group, are then used to obtain refined estimators which, when put in the diagonal matrix /)i as its diagonal elements, are such that/5/)i/5 t has correlation-matrix structure.