Uniform strong consistency of robust estimators

In the robustness framework, the distribution underlying the data is not totally specified and, therefore, it is convenient to use estimators whose properties hold uniformly over the whole set of possible distributions. In this paper, we give two general results on uniform strong consistency and apply them to study the uniform consistency of some classes of robust estimators over contamination neighborhoods. Some instances covered by our results are Huber's M-estimators, quantiles, or generalized S-estimators.