Consistency for constrained maximum likelihood estimation and clustering based on mixtures of elliptically-symmetric distributions under general data generating processes

The consistency of the maximum likelihood estimator for mixtures of elliptically-symmetric distributions for estimating its population version is shown, where the underlying distribution P is nonparametric and does not necessarily belong to the class of mixtures on which the estimator is based. In a situation where P is a mixture of well enough separated but nonparametric distributions it is shown that the components of the population version of the estimator correspond to the well separated components of P . This provides some theoretical justification for the use of such estimators for cluster analysis in case that P has well separated subpopulations even if these subpopulations differ from what the mixture model assumes.