Chapter VII - The MSE Neglecting the Prior Assumptions

Abstract

The mean square error (MSE) neglecting prior assumptions has properties quite different from the average MSE. The average MSE of the Bayes estimator (BE) is smaller than that of the least square estimator. One BE has a smaller average MSE than another if the prior information is more precise. The MSE of the BE or a mixed estimator neglecting the prior observations is smaller than that of the least square estimator provided that the ß parameters lie on an ellipsoid about the prior mean. A more precise prior mean does not automatically imply that one estimator has a smaller MSE neglecting prior assumptions. The chapter presents a calculation of three alternative forms of the MSE of the BE without averaging over the prior. It reviews the corresponding results for the mixed estimator. The chapter also discusses the form of the ellipsoids where the conditional MSE of the BE is smaller than that of the least square (LS) and the average MSE.