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2008

A Minimax Chebyshev Estimator for Bounded Error Estimation

11 years 5 months ago
A Minimax Chebyshev Estimator for Bounded Error Estimation
We develop a nonlinear minimax estimator for the classical linear regression model assuming that the true parameter vector lies in an intersection of ellipsoids. We seek an estimate that minimizes the worst-case estimation error over the given parameter set. Since this problem is intractable, we approximate it using semidefinite relaxation, and refer to the resulting estimate as the relaxed Chebyshev center (RCC). We show that the RCC is unique and feasible, meaning it is consistent with the prior information. We then prove that the constrained least-squares (CLS) estimate for this problem can also be obtained as a relaxation of the Chebyshev center, that is looser than the RCC. Finally, we demonstrate through simulations that the RCC can significantly improve the estimation error over the CLS method.
Yonina C. Eldar, Amir Beck, Marc Teboulle
Added 16 Dec 2010
Updated 16 Dec 2010
Type Journal
Year 2008
Where TSP
Authors Yonina C. Eldar, Amir Beck, Marc Teboulle
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