Robust MSE Estimation: New Methods for Old Problems
Prof. Yonina Eldar, Technion, Israel Institute of Technology, Haifa, Israel
In this talk, we introduce a new framework for linear estimation, that is aimed at developing effective linear estimators which minimize criteria that are directly related to the estimation error. In developing this framework, we exploit recent results in convex optimization theory and nonlinear programming. As we demonstrate, this framework leads to new, powerful, estimation methods that can significantly outperform existing estimators such as least-squares and Tikhonov regularization.
We begin by developing an estimator that minimizes the worst-case mean-squared error (MSE) over a given region of uncertainty. We then extend this estimator to include cases in which the model matrix H is not known precisely. Next, we consider competitive minimax regret approaches to linear estimation, in which we seek estimators with performance that is as close as possible to that of the optimal linear estimator that minimizes the MSE when x is assumed to be known. Finally, we extend these ideas to multichannel estimation, and present several examples of applications.
Prof. Yonina Eldar, Technion, Israel Institute of Technology, Haifa, Israel
Seminar • 18 February 2004 • EPFL, BM.5.202
More Info ...Abstract The problem of estimating a set of unknown deterministic parameters x observed through a linear transformation H and corrupted by additive noise, i.e., y = H x + w, arises in a large variety of areas in science and engineering. Owing to the lack of statistical information about the parameters x, the estimated parameters are typically chosen to optimize a criterion based on the observed signal y. For example, the celebrated least-squares estimator is chosen to minimize the Euclidian norm of the data error y - y. However, in an estimation context, the objective typically is to minimize the size of the estimation error x - x, rather than that of the data error y - y. It is well known that estimators based on minimizing a data error can lead to a large estimation error.In this talk, we introduce a new framework for linear estimation, that is aimed at developing effective linear estimators which minimize criteria that are directly related to the estimation error. In developing this framework, we exploit recent results in convex optimization theory and nonlinear programming. As we demonstrate, this framework leads to new, powerful, estimation methods that can significantly outperform existing estimators such as least-squares and Tikhonov regularization.
We begin by developing an estimator that minimizes the worst-case mean-squared error (MSE) over a given region of uncertainty. We then extend this estimator to include cases in which the model matrix H is not known precisely. Next, we consider competitive minimax regret approaches to linear estimation, in which we seek estimators with performance that is as close as possible to that of the optimal linear estimator that minimizes the MSE when x is assumed to be known. Finally, we extend these ideas to multichannel estimation, and present several examples of applications.