Some Comments on the Minimum mean Square Error as a Criterion of Estimation

摘要

It is shown that estimators obtained by MMSE (minimizing the mean square error) may not have optimum properties with respect to other criteria such as PN (probability of nearness to the true value in the sense of Pitman) or PC (probability of concentration around the true value). In particular, a detailed study is made of estimators obtained by shrinking the minimum variance unbiased estimators to reduce the MSE. It is suggested that because of mathematical convenience and some intuitive considerations, MMSE could be used as a primitive postulate to derive estimators, but their acceptability should be judged on more intrinsic criteria such as PN and PC. (Author)