Robust statistical inference: Weighted likelihoods or usual M-Estimation?

We review the weighted likelihood estimating equations methodology introduced by Markatou, Basu and Lindsay (1995). and Basu, Markatou and Lindsay (1995) and compare it, in the case of symmetric and asymmetric contamination, with Huber's M-estimators of location. The simulation study shows that the weighted likelihood estimating equations estimator is at least as competitive as Huber's M-estimators in the case of symmetric contamination. In the case of asymmetric contamination it may be superior than Huber's M-estimators.