Mes performance of the minimum mean squared error estimators in a linear regression model when relevant regressors are omitted

Abstract

In this paper, we consider a linear regression model when relevant regressors are omitted. We derive the explicit formulae of the mean squared errors (MSE's) of the feasible minimum MSE (FMMSE) estimator and the adjusted FMMSE (AFMMSE) estimator. By numerical evaluations, we compare the MSE performances of the FMMSE and AFMMSE estimators with those of the Stein-rule (SR) and positive-part Stein-rule (PSR) estimators. It is shown that when there are omitted regressors, the MSE performances of the AFMMSE and PSR estimators are comparable when the number of regressors included in the specified model (sayk 1) is larger than or equal to 8, and the MSE performance of the AFMMSE estimator is better than that of the PSR estimator when k 1≤5 and the model misspecification is severe.