GENERALIZED LINEAR ESTIMATE OF FUNCTIONS OF RANDOM MATRIX ARGUMENTS.

The optimal linear estimation problem in a generalized formulation is considered for a function of observational data matrix being a sum of random matrix signals and of a matrix of observation errors or noise. The criterion of optimality is the minimization of the penalty which is a linear combination of the squares of the norms of two kinds of errors: of the error matrix which would take place in estimation without noise and of the matrix of actual estimating errors. Results are applicable also in the case of deficient rank of covariance matrices and/or of signal model. Correlation of signals with the noise is allowed. A priori statistics of signals can be incorporated to improve the estimates. It is shown that different known generalizations of least squares estimates are special cases of the minimum penalty estimate.