This paper introduces a new class of robust estimators for the
linear regression model. They are weighted least squares estimators, with
weights adaptively computed using the empirical distribution of the residuals
of an initial robust estimator. It is shown that under certain general
conditions the asymptotic breakdown points of the proposed estimators are not
less than that of the initial estimator, and the finite sample breakdown point
can be at most $1/n$ less. For the special case of the least median of squares
as initial estimator, hard rejection weights and normal errors and carriers,
the maximum bias function of the proposed estimators for point-mass
contaminations is numerically computed, with the result that there is almost no
worsening of bias. Moreover–and this is the original contribution of
this paper–if the errors are normally distributed and under fairly
general conditions on the design the proposed estimators have full asymptotic
efficiency. A Monte Carlo study shows that they have better behavior than the
initial estimators for finite sample sizes.