Unbiased Estimation of the MSE Matrix of Stein-Rule Estimators, Confidence Ellipsoids, and Hypothesis Testing

We first present an unbiased estimator of the MSE matrix of the Stein-rule estimator of the coefficient vector in a normal linear regression model. The Steinrule estimator can be used with both its estimated MSE matrix and with the least-squares MSE matrix to form confidence ellipsoids. We derive the approximate expected squared volumes and coverage probabilities of these confidence sets and discuss their ranking. These results can be applied to the conditional prediction of the mean of the endogenous variable. We also consider the power of <italic>F</italic>-tests which employ the Stein-rule estimator in place of the least-squares estimator.