Asymptotics for one-step m-estimators in regression with application to combining efficiency and high breakdown point

In the linear regression model, a one-step version of the M-estimator M n starting with an initial estimator T n is proposed which inherits the efficiency properties of M n and the breakdown-point of T n respectively; this even in the case that the rate of consistency of T n is lower than Such results suggest a potentially valuable method for combining high efficiency with high breakdown point. They follow from a general asymptotic linearity result which holds for M -estimators with kernels which are not everywhere differentiable. Keywords: M-estimatorbreakdown pointasymptotic linearitylinear regression 1This research was partially supported by NSF grant DMS 85-03785 and by a Miller Visiting Professorship at University of Illinois 1This research was partially supported by NSF grant DMS 85-03785 and by a Miller Visiting Professorship at University of Illinois Notes 1This research was partially supported by NSF grant DMS 85-03785 and by a Miller Visiting Professorship at University of Illinois