In the robust statistics literature, a wide variety of models has been developed 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 variables are present. What we propose in this paper is a simple solution to this involving the replacement of the subsampling 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.
