A theory for linear estimators minimizing the variance of the error squared (Corresp.)

A study of linear estimators that minimize the variance of the error squared is reported. A projection principle and a sufficiency test establish and verify minimality. When the signal process and the data process are jointly Gaussian, the problem is completely solved for unique absolutely minimizing operators, which are found to be a cascade of the classical minimum-mean-squared error estimator and an amplifier.