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量在估计其总体版本时的一致性，其中底层分布$P$是非参数的，且不一定属于估计量所基于的混合类别。在$P$是充分分离但非参数分布的混合情形下，我们证明了估计量总体版本的各分量对应于$P$的分离分量。这为$P$存在充分分离子总体时（即使这些子总体与混合模型假设不同）将该类估计量用于聚类分析提供了一定的理论依据。