|M.Sc Student||Ben-Haim Zvi|
|Subject||Blind Minimax and Maximum Set Estimators: Improving on|
|Department||Department of Electrical Engineering||Supervisor||Professor Yonina Eldar|
We consider the problem of estimating an
unknown, deterministic parameter vector, observed through colored Gaussian
noise. This classical problem is generally solved using the least-squares
(LS) estimator. We explore alternatives to this approach, and demonstrate
analytically that our techniques outperform the LS estimator in terms of
mean-squared error (MSE). We begin by
presenting blind minimax estimators (BMEs), which consist of a minimax
estimator on a parameter set which is itself estimated from measurements. We
demonstrate analytically that the BMEs dominate the least-squares estimator,
i.e., they always achieve lower MSE. We explore the relation of this
approach to the James-Stein estimator, and demonstrate its advantage over
various other Stein-type estimators.
We next consider the problem of finding a linear estimator whose MSE does not exceed a given maximum. We develop estimators guaranteeing the required error for as large a parameter set as possible and for as large a noise level as possible. We discuss methods for finding these estimators and demonstrate that in many cases, the proposed estimators outperform the LS estimator.