Asymptotic behavior of iterative m-estimators for the linear model

In this paper, we study the M-estimators for the linear model when they are computed by a class of numerical iterative procedures. This class includes the usual method of Newton-Raphson, iteratively reweighted least squares and iterative winsorization. We show that under mild conditions, the numerical iterative procedures converge and the resulting estimators are consistent and asymptotically normal.