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