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This paper studies identifiability and convergence behaviors for parameters of multiple types in finite mixtures, and the effects of model fitting with extra mixing components.
Identifiability of mixtures
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Identifiability of finite mixtures
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An algorithm for finding the basis elements of the residue class ring of a zero dimensional polynomial ideal
B. Buchberger · 1965
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S. J. Yakowitz and J. D. Spragins · 1968
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Statistics of directional data
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Identifiability of finite mixtures of von mises distributions
Y. S. Hsu, M. D. Fraser, and J. J. Walker · 1981
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Identifiability of finite mixtures for directional data
J. T. Kent · 1983
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Optimal rates of convergence for deconvolving a density
R. J. Carroll and P. Hall · 1988
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Mixture models: Inference and Applications to Clustering. Statistics: Textbooks and Monographs
G. J. McLachlan and K. E. Basford · 1988
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Fourier methods for estimating mixing densities and distributions
C. Zhang · 1990
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On the optimal rates of convergence for nonparametric deconvolution problems
J. Fan · 1991
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Optimal rate of convergence for finite mixture models
J. Chen · 1995
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Mixture models: Theory, geometry and applications
B. Lindsay · 1995
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The multivariate skew-normal distribution
A. Azzalini and A. D. Valle · 1996
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Rates of convergence for the maximum likelihood estimator in mixture models
S. van de Geer · 1996
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Assouad, Fano, and Le Cam
B. Yu · 1997
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Statistical applications of the multivariate skew-normal distribution
A. Azzalini and A. Capitanio · 1999
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Learning mixtures of Gaussians
Nonparametric inference in multivariate mixtures
P. Hall, A. Neeman, R. Pakyari, and R. Elmore · 2005
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Asymptotic Theory of Statistics and Probability
A. DasGupta · 2008
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Identifiability of parameters in latent structure models with many observed variables
E. S. Allman, C. Matias, and J. A. Rhodes · 2009
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Optimal Transport: Old and New. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathemtical Sciences]
C. Villani · 2009
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Polynomial learning of distribution families
M. Belkin and K. Sinha · 2010
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Deconvolution for the Wasserstein metric and geometric inference
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