The　robust　Huber＇s　M-estimator　is　widely　used　in　signal　and　image　processing,　classification,　and　regression.　From　an　optimization　point　of　view,　Huber＇s　M-estimation　problem　is　often　formulated　as　a　large-sized　quadratic　programming　(QP)　problem　in　view　of　its　nonsmooth　cost　function.　This　paper　presents　a　generalized　regression　estimator　which　minimizes　a　reduced-sized　QP　problem.　The　generalized　regression　estimator　may　be　viewed　as　a　significant　generalization　of　several　robust　regression　estimators　including　Huber＇s　M-estimator.　The　performance　of　the　generalized　regression　estimator　is　analyzed　in　terms　of　robustness　and　approximation　accuracy.　Furthermore,　two　low-dimensional　recurrent　neural　networks　(RNNs)　are　introduced　for　robust　estimation.　The　two　RNNs　have　low　model　complexity　and　enhanced　computational　efficiency.　Finally,　the　experimental　results　of　two　examples　and　an　application　to　image　restoration　are　presented　to　substantiate　superior　performance　of　the　proposed　method　over　conventional　algorithms　for　robust　regression　estimation　in　terms　of　approximation　accuracy　and　convergence　rate.　©　2018　IEEE.