Blind minimax estimators: improving on least-squares estimation

We consider the linear regression problem of estimating an unknown, deterministic parameter vector based on measurements corrupted by colored Gaussian noise. We present and analyze estimators based on the blind minimax approach, a technique whereby a parameter set is estimated from measurements and then used to construct a minimax estimator. We demonstrate analytically that the obtained estimators strictly dominate the least-squares estimator (LSE), i.e.. they achieve lower mean-squared error for any value of the parameter vector. Simulations show that these estimators outperform Bock's estimator, which also dominates the LSE