Minimax Regret Classifier for Imprecise Class Distributions
The Journal of Machine Learning Research
Rethinking Biased Estimation: Improving Maximum Likelihood and the Cramér–Rao Bound
Foundations and Trends in Signal Processing
Robust Linear Transmit/Receive Processing for Correlated MIMO Downlink with Imperfect CSI
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
IEEE Transactions on Signal Processing
Stochastic MV-PURE estimator: robust reduced-rank estimator for stochastic linear model
IEEE Transactions on Signal Processing
Robust transceiver optimization in downlink multiuser MIMO systems
IEEE Transactions on Signal Processing
Worst-case robust MIMO transmission with imperfect channel knowledge
IEEE Transactions on Signal Processing
Robust QoS-constrained optimization of downlink multiuser MISO systems
IEEE Transactions on Signal Processing
Robust cognitive beamforming with bounded channel uncertainties
IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing
Noninvertible gabor transforms
IEEE Transactions on Signal Processing
Competitive linear estimation under model uncertainties
IEEE Transactions on Signal Processing
Robust MMSE precoding in MIMO channels with pre-fixed receivers
IEEE Transactions on Signal Processing
On the robustness of transmit beamforming
IEEE Transactions on Signal Processing
Worst-case optimized V-BLAST receiver design for imperfect MIMO channels
MILCOM'06 Proceedings of the 2006 IEEE conference on Military communications
IEEE Transactions on Information Theory
Robust estimation in flat fading channels under bounded channel uncertainties
Digital Signal Processing
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We consider the problem of estimating, in the presence of model uncertainties, a random vector x that is observed through a linear transformation H and corrupted by additive noise. We first assume that both the covariance matrix of x and the transformation H are not completely specified and develop the linear estimator that minimizes the worst-case mean-squared error (MSE) across all possible covariance matrices and transformations H in the region of uncertainty. Although the minimax approach has enjoyed widespread use in the design of robust methods, we show that its performance is often unsatisfactory. To improve the performance over the minimax MSE estimator, we develop a competitive minimax approach for the case where H is known but the covariance of x is subject to uncertainties and seek the linear estimator that minimizes the worst-case regret, namely, the worst-case difference between the MSE attainable using a linear estimator, ignorant of the signal covariance, and the optimal MSE attained using a linear estimator that knows the signal covariance. The linear minimax regret estimator is shown to be equal to a minimum MSE (MMSE) estimator corresponding to a certain choice of signal covariance that depends explicitly on the uncertainty region. We demonstrate, through examples, that the minimax regret approach can improve the performance over both the minimax MSE approach and a "plug in" approach, in which the estimator is chosen to be equal to the MMSE estimator with an estimated covariance matrix replacing the true unknown covariance. We then show that although the optimal minimax regret estimator in the case in which the signal and noise are jointly Gaussian is nonlinear, we often do not lose much by restricting attention to linear estimators.