On approximations via convolution-defined mixture models

An often-cited fact regarding mixing or mixture distributions is that their density functions are able to approximate the density function of any unknown distribution to arbitrary degrees of accuracy, provided that the mixing or mixture distribution is sufficiently complex. This fact is often not ma...

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Bibliographic Details
Published inCommunications in statistics. Theory and methods Vol. 48; no. 16; pp. 3945 - 3955
Main Authors Nguyen, Hien D., McLachlan, Geoffrey
Format Journal Article
LanguageEnglish
Published Philadelphia Taylor & Francis 18.08.2019
Taylor & Francis Ltd
Subjects
Approximation
Convolution
Density
Economic models
Finite mixture models
Kullback-Leibler divergence
Mathematical analysis
Maximum likelihood estimation
Maximum likelihood estimators
mixing distributions
Monte Carlo simulation
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Summary:An often-cited fact regarding mixing or mixture distributions is that their density functions are able to approximate the density function of any unknown distribution to arbitrary degrees of accuracy, provided that the mixing or mixture distribution is sufficiently complex. This fact is often not made concrete. We investigate and review theorems that provide approximation bounds for mixing distributions. Connections between the approximation bounds of mixing distributions and estimation bounds for the maximum likelihood estimator of finite mixtures of location-scale distributions are reviewed.
ISSN:0361-0926
1532-415X
DOI:10.1080/03610926.2018.1487069