ON THE PERFORMANCE OF MINIMAX ESTIMATORS IN LINEAR-REGRESSION

We consider the linear regression model where prior information in form of inequalities restricts the parameter space to a compact set. The Linear Minimax estimator, which minimizes the maximum risk within the class of linear estimators, has the disadvantage that it has in general to be determined numerically. Therefore it was proposed to minimize an approximation of the maximum risk instead. The resulting so-called Quasi Minimax estimators, can be easily calculated in closed form. While both the Linear Minimax and the Quasi Minimax estimator are admissible in the class of all linear estimators, numerical studies demonstrate the superior average performance of the Quasi Minimax estimator.