A lower bound for the Mismatched Maximum Likelihood estimator

A lower bound on Mean Square Error (MSE) of the estimate of a real deterministic parameter vector under misspecified model is proposed in this paper. In particular, a lower bound on the MSE of the Mismatched Maximum Likelihood (MML) estimator is derived in closed form and its relation with the Huber limit is investigated. Two simple illustrative examples are provided. Finally, the proposed framework is applied to the estimation of the scatter matrix in the Complex Elliptically Symmetric (CES) distribution family.