Estimators as decision devices and estimation under uncertainty

Two results are presented in this paper. The first pertains to the use of the minimum mean square error (MMSE) estimator as a test statistic in an Mary decision problem. In particular, it is shown that if the cost function in an M-ary decision problem is discrete quadratic, then the MMSE estimator for the decision variable can be used as a test statistic in the decision process. The second result is concerned with the performance of a MMSE estimator when the presence of the signal is uncertain. An expression is obtained for the difference between the variance of the estimation error when the presence or absence of the signal is known and when it is not known.