Full-model estimation for non-parametric multivariate finite mixture models

Abstract

Abstract 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) by considering an upper bound on the number of components (this number being allowed to increase with the sample size). 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. The relevance of our proposal is illustrated on simulated and benchmark data.