Robust estimation on a parametric model with tests

We are interested in the problem of robust parametric estimation of a density from i.i.d observations. By using a practice-oriented procedure based on robust tests, we build an estimator for which we establish non-asymptotic risk bounds with respect to the Hellinger distance under mild assumptions on the parametric model. We prove that the estimator is robust even for models for which the maximum likelihood method is bound to fail. We also evaluate the performance of the estimator by carrying out numerical simulations for which we observe that the estimator is very close to the maximum likelihood one when the model is regular enough and contains the true underlying density.