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.

翻译：本文证明了椭圆对称分布混合的最大似然估计在其总体版本估计中的一致性，其中底层分布$P$是非参数的，且不一定属于估计所依据的混合类别。当$P$是分离足够充分但非参数分布的混合时，估计量的总体版本中的各个分量对应于$P$中充分分离的分量。这为当$P$具有充分分离的子总体时，即使这些子总体与混合模型假设的不同，此类估计在聚类分析中的应用提供了一定的理论依据。