Nonparametric consistency for maximum likelihood estimation and clustering based on mixtures of elliptically-symmetric distributions

arXiv:2311.06108v2 Announce Type: replace-cross
Abstract: 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 …

abstract arxiv class clustering distribution likelihood math.st maximum likelihood estimation population stat.ml stat.th type