Least-squares approximation of an improper by a proper correlation matrix using a semi-infinite convex program

Dirk L. Knol, Jos M.F. ten Berge

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Abstract

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.
Original languageUndefined
Place of PublicationEnschede, the Netherlands
PublisherUniversity of Twente, Faculty Educational Science and Technology
Number of pages33
Publication statusPublished - 1987

Publication series

NameOMD research report
PublisherUniversity of Twente, Faculty of Educational Science and Technology
No.87-7

Keywords

  • Least Squares Statistics
  • Estimation (Mathematics)
  • Statistical Analysis
  • IR-104195
  • Computer Software
  • Correlation
  • Algorithms

Cite this

Knol, D. L., & ten Berge, J. M. F. (1987). Least-squares approximation of an improper by a proper correlation matrix using a semi-infinite convex program. (OMD research report; No. 87-7). Enschede, the Netherlands: University of Twente, Faculty Educational Science and Technology.