Minimax estimators dominating the least-squares estimator

We present several analytical and numerical results demonstrating the superiority of minimax estimators over least-squares (LS) estimation. We show that, for any bounded parameter set, a linear minimax estimator achieves lower mean-squared error than the LS estimator, over the entire parameter set. When a parameter set is unknown, we propose to estimate the parameter set from the data, and show that in many cases, the obtained blind minimax estimator still dominates the LS estimator. The results are related to and compared with other LS-dominating estimators, such as the James-Stein estimator.