Mean square error matrix properties of Bayes estimation for incorrect prior information under misspecification

Summary: This article deals with the linear Bayes estimator (LBE) for incorrect prior assumptions under the misspecified linear regression model. In order to obtain the mean square error (MSE)-matrix properties of theLBE, we compare theMSE-matrix of theLBE averaging over the correct prior assumptions with that averaging over incorrect prior assumptions. We also compare theMSE-matrices of the ordinary least square estimator (OLSE) and theLBE under correct prior assumptions, given that the original prior assumptions are incorrect. Finally, we examine theMSE-matrix properties of theLBE in prediction problems.