Robustification of the MLE without loss of efficiency

Abstract

A robust procedure, which produces the maximum likelihood estimator when the data are in conformity with the parametric model, and generates the outlier deleted maximum likelihood estimator under the presence of extreme outliers, has obvious intuitive appeal to the practising scientist. None of the currently available robust estimators achieves this automatically. Here we propose a density-based divergence belonging to the family of disparities ([7]) where the corresponding weighted likelihood estimator ([10], [11]) exhibits this desirable behavior for proper choices of tuning parameters. Some properties of the corresponding estimation procedure are discussed and illustrated through examples. � 2011 Springer-Verlag Berlin Heidelberg.