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：对于椭球对称分布混合的最大似然估计量，本文证明了其总体版本估计的一致性，其中底层分布$P$是非参数的，且未必属于该估计量所基于的混合分布类别。在$P$为充分分离但非参数分布混合的情况下，研究表明，该估计量总体版本的分量对应于$P$中充分分离的分量。这为在$P$具有充分分离子总体时使用此类估计量进行聚类分析提供了部分理论依据，即使这些子总体与混合模型假设的分布形式存在差异。