Dominating and Admissible Mse-Bounds Using Saddle-Point Methods

We treat the problem of evaluating the performance of estimators for estimating a deterministic parameter vector x, with the mean-squared error (MSE) as the performance measure. Since the MSE depends on the unknown vector x, direct comparison between estimators is a difficult problem. Here we consider a framework for examining the MSE of different approaches based on the concepts of admissible and dominating estimators. Using a saddle-point framework we reduce these abstract concepts to a concrete convex optimization problem, which can then by analyzed by utilizing the machinery of convex optimization. Our development considers both the case of linear estimation in linear models as well as more general nonlinear models