Name
Abstract | ||
|---|---|---|
In continuation to an earlier work, we further consider the problem of robust estimation of a random vector (or signal), with an uncertain covariance matrix, that is observed through a known linear transformation and corrupted by additive noise with a known covariance matrix. While, in the earlier work, we developed and proposed a competitive minimax approach of minimizing the worst-case mean-squared error (MSE) difference regret criterion, here, we study, in the same spirit, the minimum worst-case MSE ratio regret criterion, namely, the worst-case ratio (rather than difference) between the MSE attainable using a linear estimator, ignorant of the exact signal covariance, and the minimum MSE (MMSE) attainable by optimum linear estimation with a known signal covariance. We present the optimal linear estimator, under this criterion, in two ways: The first is as a solution to a certain semidefinite programming (SDP) problem, and the second is as an expression that is of closed form up to a single parameter whose value can be found by a simple line search procedure. We then show that the linear minimax ratio regret estimator can also be interpreted as the MMSE estimator that minimizes the MSE for a certain choice of signal covariance that depends on the uncertainty region. We demonstrate that in applications, the proposed minimax MSE ratio regret approach may outperform the well-known minimax MSE approach, the minimax MSE difference regret approach, and the "plug-in" approach, where in the latter, one uses the MMSE estimator with an estimated covariance matrix replacing the true unknown covariance. |
Year | DOI | Venue |
|---|---|---|
2005 | 10.1109/TSP.2005.843701 | IEEE Transactions on Signal Processing |
Keywords | Field | DocType |
covariance matrix,minimax mse-ratio estimation,earlier work,well-known minimax mse approach,proposed minimax mse ratio,exact signal covariance,estimated covariance matrix,minimum worst-case mse ratio,minimum mse,minimax mse difference regret,mmse estimator,signal covariance uncertainty,semidefinite programming,statistics,robust estimator,uncertainty,vectors,signal processing,minimax regret,mean squared error,linear programming,linear transformation,mean square error,line search,ratio estimator,parameter estimation | Covariance function,Mathematical optimization,Minimax,Estimation of covariance matrices,Regret,Mean squared error,Covariance matrix,Mathematics,Estimator,Covariance | Journal |
Volume | Issue | ISSN |
53 | 4 | 1053-587X |
Citations | PageRank | References |
16 | 0.96 | 19 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Y.C. Eldar | 1 | 265 | 22.07 |
| Neri Merhav | 2 | 1120 | 170.28 |