In the extant literature a suggestion has been made to solve the nearest correlation matrix problem by a modified von Neumann approximation. This paper shows that obtaining the nearest positive semi-definite matrix from a given non-positivesemi- definite correlation matrix by such a method is either infeasible or suboptimal. First, if a given matrix is already positive semi-definite, there is no need to obtain any other positive semi-definite matrix closest to it. But when the given matrix is non-positive-semi-definite (Q), then a positive semi-definite matrix closest to it is needed. Then the proposed procedure fails in the absence of log(Q). But if the negative eigenvalue of Q is replaced by a zero/near-zero value, a positive semidefinite matrix is obtained, but it is not nearest to the Q matrix; there are indeed other procedures to obtain better approximation. However, the modified von Neumann approximation method yields results (although sub-optimal) and is, perhaps, one of the fastest methods most suitable to deal with larger matrices. Yet, an alternative algorithm (Fortran program available at http://www.webng.com/ economics/ncor1.txt) is provided to obtain a positive (semi-) definite matrix that performs (speed as well as accuracy-wise) much better.

Brian (2005), in his paper, makes an attempt to solve the nearest correlation matrix problem by using the Bregman matrix divergence and the von Neumann matrix divergence. Presently, we are concerned with the method (suggested by Brian Culis) that uses the von Neumann divergence.

These norms are smaller than those obtained through the (modified) von Neumann divergence procedure. Clearly, the procedure gives sub-optimal solution to the nearest correlation matrix problem.

Computational Mathematics Journal, Logistic Regression Models, Business Management, Decision Theory, Logistic Regression Programs, SPSS Nonlinear Program, Proportional Reductions, Statistical Aanalysis Software Package, Statistical Software SPSS, Squared Pearson Correlation .