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An operator theoretic approach to nonparametric mixture models. (English) Zbl 1431.62274
This research considers the distribution-free estimation of a normal mixture. In detail, in absence of any information on the distribution for each mixture component, it provides a quantification on the number of observations needed – as a function of the number of the mixture components – so that the mixture is identifiable. Additionally, this article quantifies the identifiability of mixtures with linearly independent and jointly irreducible components; it should be noted that the provided results are definite in the sense that they cannot be improved any further. An application, based on multinomial mixture models concludes this work.
MSC:
62H30 Classification and discrimination; cluster analysis (statistical aspects)
62G05 Nonparametric estimation
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