文章基本信息

标题：On strong identifiability and convergence rates of parameter estimation in finite mixtures
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作者：Nhat Ho ; XuanLong Nguyen
期刊名称：Electronic Journal of Statistics
印刷版ISSN：1935-7524
出版年度：2016
卷号：10
期号：1
页码：271-307
DOI：10.1214/16-EJS1105
语种：English
出版社：Institute of Mathematical Statistics
摘要：This paper studies identifiability and convergence behaviors for parameters of multiple types, including matrix-variate ones, that arise in finite mixtures, and the effects of model fitting with extra mixing components. We consider several notions of strong identifiability in a matrix-variate setting, and use them to establish sharp inequalities relating the distance of mixture densities to the Wasserstein distances of the corresponding mixing measures. Characterization of identifiability is given for a broad range of mixture models commonly employed in practice, including location-covariance mixtures and location-covariance-shape mixtures, for mixtures of symmetric densities, as well as some asymmetric ones. Minimax lower bounds and rates of convergence for the maximum likelihood estimates are established for such classes, which are also confirmed by simulation studies.