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A Minimax Regret Approach To Robust Beamforming

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Following the popular minimax approach, in Section II, we seek the linear estimator that minimizes the worst-case MSE over all possible values of that satisfy a weighted norm con-straint of the form for some positive definite ma-trix and constant . Here the MSE is computed by averaging over the noise and the model matrix. We first develop an ex-plicit expression for the minimax MSE

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 We propose a minimax regret approach to optimal factor demand under uncertainty. Regret is the deviation of any given decision from the optimal decision based on a specified set of possible

Maximax, Maximin and Minimax Regret

PPT - Chapter 13 Decision Analysis PowerPoint Presentation - ID:6797265

Download Citation | A minimax regret approach for robust multi-objective portfolio selection problems with ellipsoidal uncertainty sets | Since security return cannot be accurately estimated using

tive beamforming approaches that minimize a ro-bust MSE measure. Two design strategies are proposed: minimax MSE and minimax regret. We demonstrate through numerical ex-amples that the suggested mini ax beamformers can outperform several existing standard and robust methods, over a wide range of signal-to-noise ratio ( The minimax regret criterion provides less conservative solutions than the “pessimistic” approach of the maximin criterion (also used to express “robustness”). TLDR This video explores decision-making strategies without probabilities, focusing on Maximax (optimistic), Maximin (pessimistic), and Minimax Regret approaches. It introduces a payoff table with decision alternatives and states of nature. The Maximax strategy advises investing in stocks for the best payoff of 70. Maximin, the conservative approach, suggests bonds with the best

tive beamforming approaches that minimize a ro-bust MSE measure. Two design strategies are proposed: minimax MSE and minimax regret. We demonstrate through numerical ex-amples that the suggested mini ax beamformers can outperform several existing standard and robust methods, over a wide range of signal-to-noise ratio (

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Since the minimax MSE approach cannot account for a nonzero lower bound, we consider, in this case, a minimax regret method in which we seek the estimator that minimizes the worst-case difference 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.

In this paper, we investigate the problem of robust beamforming for multiple-input multiple-output (MIMO) dual-function radar-communication (DFRC) system, when tive beamforming approaches that minimize a ro-bust MSE measure. Two design strategies are proposed: minimax MSE and minimax regret. We demonstrate through numerical ex-amples that the suggested mini ax beamformers can outperform several existing standard and robust methods, over a wide range of signal-to-noise ratio (

Decision Analysis Problem Formulation Decision Making without Probabilities

Minimax regret (Savage, Journal of the American Statistical Association 46, 55–67, 1951) is the principle of optimizing worst-case loss relative to some measure of unavoidable risk. In statistical decision theory, it provides a non-Bayesian alternative to minimax. It differs from minimax by fulfilling von Neumann–Morgenstern independence but exhibiting menu This paper discusses the design of broadband beamformers with an arbitrary spatial directivity pattern, which are robust against unknown gain and phase errors in the microphone array characteristics. In Section II, the far-field broadband beamforming problem is introduced, and some definitions and notational conventions are given.

Since the MSE depends on the signal power, which is unknown, we develop competitive beamforming approaches that minimize a robust MSE measure. Two design strategies are proposed: minimax MSE and minimax regret. Finally, a practical example based on real market data is presented to illustrate the effectiveness of the proposed model and the algorithm. Compared with the traditional robust portfolio model based on minimax robustness, the robust minimax regret optimal solutions proposed in this paper have better performance on several evaluation We instead propose an alternative method called Minimax Regret Optimization (MRO), and show that under suitable conditions, this method achieves uniformly low regret across all test distributions.

Please cite this article as: P. Xidonas , G. Mavrotas , C. Hassapis , C. Zopounidis , Robust multiob-jective portfolio optimization: A minimax regret approach, European Journal of Operational Research (2017), doi: 10.1016/j.ejor.2017.03.041 This is a PDF Þle of an unedited manuscript that has been accepted for publication. Uncertainty is ubiquitous in optimization problems, leading to numerous frame- works for handling it. This paper revisits the famous minimax regret criterion within robust optimization. In essence, this criterion arises from two key motiva- tions in decision-making under uncertainty: (i) the common human tendency to regret choices especially if a better option is discovered later; and

We propose a minimax regret approach to optimal factor demand under uncertainty. Regret is the deviation of any given decision from the optimal decision based on a specified set of possible scenarios This letter investigates a reconfigurable intelligent surface (RIS) assisted mmWave system for wireless area positioning. We aim to optimize the worst-case loca In our work, we propose a minimax regret beamformer whose MSE is uniformly as close as possible

Minimax regret decision making is a strategic approach employed in various fields, including economics, game theory, and decision analysis. This method focuses on minimizing the maximum regret or loss that can occur when choosing from multiple alternatives in decision-making situations marked by uncertainty and multiple outcomes. The Significance of Minimax Since the MSE depends on the signal power, which is unknown, we develop competitive beamforming approaches that minimize a robust MSE measure. Two design strategies are proposed: minimax MSE and minimax regret.

The most common approach for designing robust estimation filters is the minimax MSE approach, initiated by Huber [4, 5], in which the estimation filter is chosen to maximize the worst-case MSE C. Related Work Many practical remedies to alleviate the sensitivity problem of minimum variance beamforming such as diagonal loading have been suggested in the literature [4]–[7]. More recently, ideas from the (worst-case) robust optimization [8]–[11] have been applied to robust beamforming. The basic idea is to explic-itly incorporate a model of data uncertainty in the

Since the MSE depends on the signal power, which is unknown, we develop competitive beamforming approaches that minimize a robust MSE measure. Two design strategies are proposed: minimax MSE and minimax regret. 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.

Since the minimax MSE approach cannot account for a nonzero lower bound, we consider, in this case, a minimax regret method in which we seek the estimator that minimizes the worst-case difference

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 Test yourself with questions about C6d. Maximax, Maximin and Minimax Regret from past papers in ACCA PM. We now consider two MSE-based criteria for developing robust beamformers when the steering vector is known: In Section 1.3.1 we consider a minimax MSE approach and in Section 1.3.2 we consider a minimax regret approach.

In this paper, we study robust linear estimation for the same linear model under the criterion of minimax ratio–regret, rather than the difference–regret. We present the optimal linear esti-mator, under this new criterion, in two ways: The first repre-sentation is as a solution to a certain semidefinite programming (SDP) problem. This is practically meaningful since SDP pro-grams