ROBUST ESTIMATION - A WEIGHTED MAXIMUM-LIKELIHOOD APPROACH

A weighted maximum likelihood technique is proposed for robust estimation in parametric families. The method weights points on the basis of the natural probabilistic scale for the model under consideration, and does not require invariance structure. The estimates are Fisher consistent, and asymptotically normal under generally satisfied conditions. Efficiencies are calculated for the location-scale and gamma families, and a small simulation study compares the estimator's performance to the MLE, a Huber estimate and an estimate proposed by Beran (1981) in the case of a contaminated gamma distribution. Applications to the multivariate normal family and a signal plus noise model are also considered.