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

• URL: http://arxiv.org/abs/2311.06108v4
• Date: Fri, 26 Apr 2024 09:22:12 GMT
• Title: Nonparametric consistency for maximum likelihood estimation and clustering based on mixtures of elliptically-symmetric distributions
• Authors: Pietro Coretto, Christian Hennig,
• Abstract summary: 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.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 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.

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