Unbiased estimation of the MSE matrices of improved estimators in linear regression

Stein-rule and other improved estimators have scarcely been used in empirical work. One major reason is that it is not easy to obtain precision measures for these estimators. In this paper, we derive unbiased estimators for both the mean squared error (MSE) and the scaled MSE matrices of a class of Stein-type estimators. Our derivation provides the basis for measuring the estimators' precision and constructing confidence bands. Comparisons are made between these MSE estimators and the least squares covariance estimator. For illustration, the methodology is applied to data on energy consumption.