Asymptotics of reweighted estimators of multivariate location and scatter

We investigate the asymptotic behavior of a weighted sample mean and covari ance, where the weights are determined by the Mahalanobis distances with re spect to initial robust estimators. We derive an explicit expansion for the weighted estimators. From this expansion it can be seen that reweighting d oes not improve the rate of convergence of the initial estimators. We also show that if one uses smooth S-estimators to determine the weights, the wei ghted estimators are asymptotically normal. Finally, we will compare the ef ficiency and local robustness of the reweighted S-estimators with two other improvements of S-estimators: T-estimators and constrained M-estimators.