A Chebyshev robust estimator in regularization regression with bounded noise

In this paper, we consider the classical linear regression model for the estimation of the parameter vector, where the noise of the observation is norm-bounded. The feasible parameter set (FPS) is constructed through all admissible solution to the linear system. Because the Chebyshev center of FPS is in fact the vector that minimizes the worst-case estimation error, we look forward to finding it as a robust estimation of the unknown parameter. In this paper, we verify that the Chebyshev center of FPS on real plane can be represented by a set of finite points, so the strict Chebyshev center can be calculated via a quadratically constrained linear program (QCLP). Then, an approximate Chebyshev center (ACC) estimator via the projections of the FPS to all coordinate planes is proposed. A numerical example shows the performance of the ACC estimator.