We consider $M$-estimators defined by minimization of a convex criterion function, not necessarily smooth. Our asymptotic results generalize some of those concerning the LAD estimators. We establish a Bahadur-type strong approximation and bounds on the rate of convergence.
"Asymptotics for $M$-Estimators Defined by Convex Minimization." Ann. Statist. 20 (3) 1514 - 1533, September, 1992. https://doi.org/10.1214/aos/1176348782