A Robust Adaptive Modified Maximum Likelihood Estimator for the Linear\n Regression Model

In linear regression, the least squares (LS) estimator has certain optimality\nproperties if the errors are normally distributed. This assumption is often\nviolated in practice, partly caused by data outliers. Robust estimators can\ncope with this situation and thus they are widely used in practice. One example\nof robust estimators for regression are adaptive modified maximum likelihood\n(AMML) estimators (Donmez, 2010). However, they are not robust to $x$ outliers,\nso-called leverage points. In this study, we propose a new regression estimator\nby employing an appropriate weighting scheme in the AMML estimation method. The\nresulting estimator is called robust AMML (RAMML) since it is not only robust\nto y outliers but also to x outliers. A simulation study is carried out to\ncompare the performance of the RAMML estimator with some existing robust\nestimators such as MM, least trimmed squares (LTS) and S. The results show that\nthe RAMML estimator is preferable in most settings according to the mean\nsquared error (MSE) criterion. Two data sets taken from the literature are also\nanalyzed to show the implementation of the RAMML estimation methodology.\n