MSE-RATIO REGRET ESTIMATION WITH BOUNDED DATA UNCERTAINTIES (ThuAmOR2)

Author(s) : Yonina Eldar (Technion, Israel)

Abstract : We consider the problem of robust estimation of a deterministic bounded parameter vector $\bx$ in a linear model. While in an earlier work, we proposed a minimax estimation approach in which we seek the estimator that minimizes the worst--case mean-squared error (MSE) {\em difference regret} over all bounded vectors $\bx$, here we consider an alternative approach, in which we seek the estimator that minimizes the worst--case MSE {\em ratio regret}, namely, the worst--case {\it ratio} between the MSE attainable using a linear estimator ignorant of $\bx$, and the minimum MSE attainable using a linear estimator that knows $\bx$. The rational behind this approach is that the value of the difference regret may not adequately reflect the estimator performance, since even a large regret should be considered insignificant if the value of the optimal MSE is relatively large.

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