The mathematical complexity of the minimum mean square estimators made inevitable the consideration of suboptimal solutions, such as the linear minimum mean square estimators. The compromise between performance and complexity can be in general less serious if the estimator that will substitute the optimum one is polynomial. If the minimum mean square estimator happens to be equal to a polynomial one, the polynomial substitution does not involve any compromise with respect to performance. Balakrishnan [1] found a necessary and sufficient condition satisfied by the joint characteristic functions of observations and variable to be estimated, so that the m.m.s. estimiate is a polynomial. The equivalent relationships in this case were found in the present paper. A matrix expression of the error difference from two different m.m.s. polynomial estimators was also found. This form involves much fewer calculations than required for finding separately the two errors.