  We observe a $n$-sample, the distribution of which is assumed to belong, or
at least to be close enough, to a given mixture model. We propose an estimator
of this distribution that belongs to our model and possesses some robustness
properties with respect to a possible misspecification of it. We establish a
non-asymptotic deviation bound for the Hellinger distance between the target
distribution and its estimator when the model consists of a mixture of
densities that belong to VC-subgraph classes. Under suitable assumptions and
when the mixture model is well-specified, we derive risk bounds for the
parameters of the mixture. Finally, we design a statistical procedure that
allows us to select from the data the number of components as well as suitable
models for each of the densities that are involved in the mixture. These models
are chosen among a collection of candidate ones and we show that our selection
rule combined with our estimation strategy result in an estimator which
satisfies an oracle-type inequality.
