  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.
