Approximate linear minimax estimation in regression analysis with ellipsoidal constraints

The linear regression model is considered where the parameter space is restricted to an ellipsoid. It is shown that within the class of heterogeneous linear estimators for β there exists a unique sequence converging to an exact (but in general not explicitly known) linear minimax estimator. Error bounds are derived, which can be used to determine a linear minimax estimator up to any degree of approximation. Specific attention is paid to a numerical method for solving the minimax problem.