Risk Comparison of Improved Estimators in a Linear Regression Model with MultivariatetErrors under Balanced Loss Function

[摘要] Under a balanced loss function, we derive the explicit formulae of the risk of the Stein-rule (SR) estimator, thepositive-part Stein-rule (PSR) estimator, the feasible minimum mean squared error (FMMSE) estimator, and the adjusted feasibleminimum mean squared error (AFMMSE) estimator in a linear regression model with multivariateterrors. The results showthat the PSR estimator dominates the SR estimator under the balanced loss and multivariateterrors. Also, our numerical resultsshow that these estimators dominate the ordinary least squares (OLS) estimator when the weight of precision of estimation islarger than about half, and vice versa. Furthermore, the AFMMSE estimator dominates the PSR estimator in certain occasions.

[学科分类] 应用数学