A new class of robust regression estimators is proposed that forms an alternative to traditional robust one-step estimators and that achieves the <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$\sqrt{n}$</EquationSource> </InlineEquation> rate of convergence irrespective of the initial estimator under a wide range of distributional assumptions. The proposed reweighted least...</equationsource></inlineequation>