Parameter estimator based on a minimum discrepancy criterion: a Bayesian approach

A new estimation criterion based on the discrepancy between the estimator´s error covariance and its information lower bound is proposed. This discrepancy measure criterion tries to take the information content of the observed data into account. A minimum discrepancy estimator (MDE) is then obtained under a linearity assumption. This estimator is shown to be equivalent to the maximum likelihood estimator (MLE), if one assumes that a linear efficient estimator exists and the prior distribution of parameters is uniform. Moreover, it is equivalent to the minimum variance unbiased estimator (MVUE) if the MDE is required to be unbiased. Illustrative examples of MDE and its comparisons with other estimators are given