On Minimax Estimation in Linear Regression Models with Ellipsoidal Constraints

We consider the simultaneous linear minimax estimation problem in linear models with ellipsoidal constraints imposed on the unknown parameter. Using convex analysis we derive necessary and sufficient optimality conditions for a matrix to define the best linear minimax estimator. For certain regions of the set of characteristics of the linear models and the constraints we exploit these optimality conditions and get explicit formulae for best linear minimax estimators.