MSE Performance of the Weighted Average Estimators Consisting of Shrinkage Estimators

In this paper we consider a regression model and propose estimators which are the weighted averages of two estimators among three estimators; the Stein-rule (SR), minimum mean squared error (MMSE) and the adjusted minimum mean squared error (AMMSE) estimators. We derive the formula for the mean squared error (MSE) of the proposed estimators. It is shown by numerical evaluations that one of the proposed estimators has smaller mean squared error (MSE) than the positive-part Stein-rule (PSR) estimator over a moderate region of parameter space when the number of the regression coefficients is small (i.e., 3). Also, its MSE performance is comparable to the PSR estimator even when the number of the regression coefficient is not so small.