  In this paper we propose a family of robust estimates for isotonic
regression: isotonic M-estimators. We show that their asymptotic distribution
is, up to an scalar factor, the same as that of Brunk's classical isotonic
estimator. We also derive the influence function and the breakdown point of
these estimates. Finally we perform a Monte Carlo study that shows that the
proposed family includes estimators that are simultaneously highly efficient
under gaussian errors and highly robust when the error distribution has heavy
tails.
