By Topic

Robust mean-squared error estimation in the presence of model uncertainties

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$31 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

3 Author(s)
Eldar, Y.C. ; Dept. of Electr. Eng., Technion Israel Inst. of Technol., Haifa, Israel ; Ben-Tal, A. ; Nemirovski, A.

We consider the problem of estimating an unknown parameter vector x in a linear model that may be subject to uncertainties, where the vector x is known to satisfy a weighted norm constraint. We first assume that the model is known exactly and seek the linear estimator that minimizes the worst-case mean-squared error (MSE) across all possible values of x. We show that for an arbitrary choice of weighting, the optimal minimax MSE estimator can be formulated as a solution to a semidefinite programming problem (SDP), which can be solved very efficiently. We then develop a closed form expression for the minimax MSE estimator for a broad class of weighting matrices and show that it coincides with the shrunken estimator of Mayer and Willke, with a specific choice of shrinkage factor that explicitly takes the prior information into account. Next, we consider the case in which the model matrix is subject to uncertainties and seek the robust linear estimator that minimizes the worst-case MSE across all possible values of x and all possible values of the model matrix. As we show, the robust minimax MSE estimator can also be formulated as a solution to an SDP. Finally, we demonstrate through several examples that the minimax MSE estimator can significantly increase the performance over the conventional least-squares estimator, and when the model matrix is subject to uncertainties, the robust minimax MSE estimator can lead to a considerable improvement in performance over the minimax MSE estimator.

Published in:

Signal Processing, IEEE Transactions on  (Volume:53 ,  Issue: 1 )