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：本文证明了基于椭球对称分布混合的最大似然估计量具有一致性，可估计其总体版本，其中潜在分布$P$是非参数的，且不必属于估计所基于的混合类别。当$P$为充分分离但非参数分布的混合时，研究表明估计量总体版本的各个分量对应于$P$的充分分离分量。这为当$P$具有充分分离子总体时（即使这些子总体与混合模型假设不同）在聚类分析中使用此类估计量提供了一定的理论依据。