We are interested in the problem of robust parametric estimation of a density
from n 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 show that the estimator is robust even for models for
which the maximum likelihood method is bound to fail. A numerical simulation
illustrates its robustness properties. When the model is true and regular
enough, we prove that the estimator is very close to the maximum likelihood
one, at least when the number of observations n is large. In particular, it
inherits its efficiency. Simulations show that these two estimators are almost
equal with large probability, even for small values of n when the model is
regular enough and contains the true density.Comment: Published at http://dx.doi.org/10.3150/15-BEJ706 in the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
