The traditional pretest estimator

We consider the problem of estimating k coefficients of interest in a linear regression model when the $(k + 1)$st coefficient is of no interest. The traditional pretest estimator is a two-step estimator of the coefficients of interest based on a t-test for the $(k + 1)$st coefficient. We study the behaviorof this estimator. Questions of admissibility, risk, and regret are addressed.