Interaction between estimator and estimation criteria

In this paper, we investigate the relationship between the location of an optimal estimator of a random variable and the corresponding estimation criterion. A "physical" interpretation of this relationship is presented. In particular, the interaction between the locations of optimal estimators and the corresponding minimum mean p-value (p>1) error costs is revealed. Accordingly, we propose an estimation error spectrum to examine the preference of estimators. Also, we can combine multiple estimators into a new one with a predictable compromised estimation performance. An illustrative example is also presented.