ON A RELATIONSHIP BETWEEN MINIMAX-LINEAR AND ADMISSIBLE ESTIMATORS IN LINEAR-REGRESSION

Minimax-linear estimation with respect to the quadratic risk is considered among the class of linear estimators of beta, under the linear regression model M = {y, Xbeta, sigma2I}. New classes of minimax-linear estimators of beta are derived among certain subsets of linear estimators, which are simple from the point of view of minimax estimation. The admissible linear estimators of beta under M are then characterized via these classes of minimax-linear estimators, and the relationship between the minimax-linear and admissible estimators of beta is examined. Various properties of linear admissible estimators follow readily from this new characterization.