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Mathematics > Statistics Theory
Title: Nonparametric consistency for maximum likelihood estimation and clustering based on mixtures of elliptically-symmetric distributions
(Submitted on 10 Nov 2023 (v1), last revised 26 Apr 2024 (this version, v4))
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.
Submission history
From: Pietro Coretto [view email][v1] Fri, 10 Nov 2023 15:20:39 GMT (33kb,D)
[v2] Mon, 4 Mar 2024 17:03:00 GMT (241kb,D)
[v3] Sat, 9 Mar 2024 14:52:36 GMT (227kb,D)
[v4] Fri, 26 Apr 2024 09:22:12 GMT (229kb,D)
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