טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentBen-Haim Zvi
SubjectBlind Minimax and Maximum Set Estimators: Improving on
Least-Squares Estimation
DepartmentDepartment of Electrical Engineering
Supervisor Professor Yonina Eldar


Abstract

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.