Complementing Rukhin's  investigations, the mean squared error of members of a family of preliminary-test estimators and members of the basic family of shrinkage estimators are compared. The reference point is Stein's  estimator that is contained in both classes. It turns out that Stein's estimator has certain qualitative optimality properties among the preliminary-test estimators. But it also turns out that, while Rukhin's 4% maxim in the minimax shrinkage class is well known and frequently cited, without minimaxity greater improvements can be achieved in his local sense by estimators coming from the preliminary-test class. This underlines another aspect of Stein's original insight. Most of our findings are presented graphically.
- preliminary-test and shrinkage estimators
- quadratiç risk
ASJC Scopus subject areas
- Statistics and Probability
- Modelling and Simulation
- Statistics, Probability and Uncertainty