  This paper addresses the problem of full model estimation for non-parametric
finite mixture models. It presents an approach for selecting the number of
components and the subset of discriminative variables (i.e., the subset of
variables having different distributions among the mixture components). The
proposed approach considers a discretization of each variable into B bins and a
penalization of the resulting log-likelihood. Considering that the number of
bins tends to infinity as the sample size tends to infinity, we prove that our
estimator of the model (number of components and subset of relevant variables
for clustering) is consistent under a suitable choice of the penalty term.
Interest of our proposal is illustrated on simulated and benchmark data.
