Shrinkage estimation for the difference between a control and treatment mean

Abstract

Estimation for the difference between a control and treatment mean in the one-way model when it is suspected but uncertain that the two mean values are equal is studied. A preliminary-test (pre-test) estimator and a shrinkage estimator after pre-test are proposed. Both the optimal level of significance for the pre-test estimator and optimal value of shrinkage coefficient for the pre-test shrinkage estimator are obtained on the basis of a regret function. The pre-test estimator performs better than the pre-test shrinkage estimator over a small region around the origin; however, the pre-test shrinkage estimator performs better than the pre-test estimator outside the dominance region, and the dominance region of the pre-test shrinkage estimator is larger than that of the pre-test estimator. Therefore, if the performance outside the dominance region and the size of dominance region are taken into account for comparison, then the pre-test shrinkage estimator is preferable to the pre-test estimator.