Robust maximum likelihood estimation in the linear model

This paper addresses the problem of maximum likelihood parameter estimation in linear models affected by Gaussian noise, whose mean and covariance matrix are uncertain. The proposed estimate maximizes a lower bound on the worst-case (with respect to the uncertainty) likelihood of the measured sample, and is computed solving a semidefinite optimization problem (SDP). The problem of linear robust estimation is also studied in the paper, and the statistical and optimality properties of the resulting linear estimator are discussed. (C) 2001 Elsevier Science Ltd. All rights reserved.