ERIC Number: ED310118
Record Type: Non-Journal
Publication Date: 1987-Oct
Reference Count: N/A
Least-Squares Approximation of an Improper by a Proper Correlation Matrix Using a Semi-Infinite Convex Program. Research Report 87-7.
Knol, Dirk L.; ten Berge, Jos M. F.
An algorithm is presented for the best least-squares fitting correlation matrix approximating a given missing value or improper correlation matrix. The proposed algorithm is based on a solution for C. I. Mosier's oblique Procrustes rotation problem offered by J. M. F. ten Berge and K. Nevels (1977). It is shown that the minimization problem belongs to a certain class of convex programs in optimization theory. A necessary and sufficient condition for a solution to yield the unique global minimum of the least-squares function is derived from a theorem by A. Shapiro (1985). A computer program was implemented to yield the solution of the minimization problem with the proposed algorithm. This empirical verification of the condition indicates that the occurrence of non-optimal solutions with the proposed algorithm is very unlikely. Two tables present values using J. de Leeuw's target matrix. (Author/SLD)
Descriptors: Algorithms, Computer Software, Correlation, Estimation (Mathematics), Least Squares Statistics, Statistical Analysis
Faculty Library, Department of Education, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands.
Publication Type: Reports - Evaluative
Education Level: N/A
Authoring Institution: Twente Univ., Enschede (Netherlands). Dept. of Education.