Bounded Error Estimation: A Chebyshev Center Approach

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 then demonstrate through simulations that the RCC can significantly improve the estimation error over the conventional constrained least-squares method.