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Robust estimators are widely used in regression analysis when the normality assumption is not satisfied. One example of robust estimators for regression is adaptive modified maximum likelihood (AMML) estimators [Donmez A. Adaptive estimation and hypothesis testing methods [dissertation]. Ankara: METU; 2010]. However, they are not robust to x outliers, so-called leverage points. In this study, we propose a new estimator called robust AMML (RAMML) which 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 estimators with some existing robust estimators. The results show that the RAMML estimators are preferable in most of the 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. [ABSTRACT FROM AUTHOR]