Weighted M-estimators for multivariate clustered data: theory and   simulation results
  We study weighted M-estimators for $\mathbb{R}^d$-valued clustered data and give sufficient conditions for their consistency. Their asymptotic normality is established with estimation of the asymptotic covariance matrix. We address the robustness of these estimators in terms of their breakdown point. Comparison with the unweighted case is performed with some numerical studies. They highlight that optimal weights maximizing the relative efficiency have a bad impact on the breakdown point. 
Mohammed El Asri, Delphine Blanke and Edith Gabriel
math.ST stat.TH