Robust MSE Estimation: New Methods for Old Problems

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. However, in an estimation context, the objective
typically is to minimize the size of the estimation error,
rather than that of the data error. 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.

http://www.ee.technion.ac.il/Sites/People/YoninaEldar/