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The consistency of the maximum likelihood estimator for mixtures ofelliptically-symmetric distributions for estimating its population version isshown, where the underlying distribution $P$ is nonparametric and does notnecessarily belong to the class of mixtures on which the estimator is based. Ina situation where $P$ is a mixture of well enough separated but nonparametricdistributions it is shown that the components of the population version of theestimator correspond to the well separated components of $P$. This providessome theoretical justification for the use of such estimators for clusteranalysis in case that $P$ has well separated subpopulations even if thesesubpopulations differ from what the mixture model assumes.

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