Separation theorems for singular values of matrices and their applications in multivariate analysis

C. Radhakrishna Rao

Journal of Multivariate Analysis, 1979, vol. 9, issue 3, 362-377

Abstract: Separation theorems for singular values of a matrix, similar to the Poincaré separation theorem for the eigenvalues of a Hermitian matrix, are proved. The results are applied to problems in approximating a given r.v. by an r.v. in a specified class. In particular, problems of canonical correlations, reduced rank regression, fitting an orthogonal random variable (r.v.) to a given r.v., and estimation of residuals in the Gauss-Markoff model are discussed. In each case, a solution is obtained by minimizing a suitable norm. In some cases a common solution is shown to minimize a wide class of norms known as unitarily invariant norms introduced by von Neumann.

Keywords: Matrix; approximations; unitarily; invariant; norm; canonical; correlations; multivariate; linear; regression; estimation; of; residuals (search for similar items in EconPapers)
Date: 1979
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Citations: View citations in EconPapers (7)

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