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Abstract
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.
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
