Anderson and Rubin and McDonald have proposed a correlation-preserving method of factor scores prediction which minimizes the trace of a residual covariance matrix for variables. Green has proposed a correlation-preserving method which minimizes the trace of a residual covariance matrix for factors. Krijnen, Wansbeek and Ten Berge have proposed minimizing the determinant rather than the trace of the latter covariance matrix, and offered an iterative procedure to that effect. In the present paper it is shown that the iterative procedure can be replaced by a closed-form solution. When all unique variances are strictly positive, this solution is the same as McDonald's. The solution coincides with Green's solution in certain special cases, for instance, when the factors are orthogonal.
ten Berge, J. M. F., Krijnen, W. P., Wansbeek, T., & Shapiro, A. (1999). Some new results on correlation-preserving factor scores prediction methods. Linear algebra and its applications, 289(1-3), 311-318. https://doi.org/10.1016/S0024-3795(97)10007-6