Consistency for constrained maximum likelihood estimation and clustering based on mixtures of elliptically-symmetric distributions under general data generating processes
证明了当真实分布不一定是椭圆对称混合分布时，基于该分布的最大似然估计仍能估计其总体版本，且当总体分布有分离良好的子总体时，估计的组分对应这些子总体，为聚类分析提供了理论依据。
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.