Robustness for Dummies

In the robust statistics literature, a wide variety of models have been devel- oped to cope with outliers in a rather large number of scenarios. Nevertheless, a recurrent problem for the empirical implementation of these estimators is that optimization algorithms generally do not perform well when dummy vari- ables are present. What we propose in this paper is a simple solution to this involving the replacement of the sub-sampling step of the maximization procedures by a projection-based method. This allows us to propose robust estimators involving categorical variables, be they explanatory or dependent. Some Monte Carlo simulations are presented to illustrate the good behavior of the method.