An EM-Like Algorithm for Semi- and Nonparametric Estimation in Multivariate Mixtures

We propose an algorithm for nonparametric estimation for finite mixtures of multivariate random vectors that strongly resembles a true EM algorithm. The vectors are assumed to have independent coordinates conditional upon knowing from which mixture component they come, but otherwise their density fu...

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Bibliographic Details
Published in:Journal of computational and graphical statistics 2009-06, Vol.18 (2), p.505-526
Main Authors: Benaglia, Tatiana, Chauveau, Didier, Hunter, David R.
Format: Article
Language:English
Subjects:
Algorithms
Coordinate systems
Datasets
Density estimation
EM algorithm
EM-Type Algorithms
Estimating techniques
Estimation methods
Euclidean space
Identifiability
Kernel density estimation
Modeling
Multivariate analysis
Multivariate mixture
Nonparametric mixture
Parametric models
Product labeling
Sample size
Simulation
Stochastic models
Studies
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Summary:We propose an algorithm for nonparametric estimation for finite mixtures of multivariate random vectors that strongly resembles a true EM algorithm. The vectors are assumed to have independent coordinates conditional upon knowing from which mixture component they come, but otherwise their density functions are completely unspecified. Sometimes, the density functions may be partially specified by Euclidean parameters, a case we call semiparametric. Our algorithm is much more flexible and easily applicable than existing algorithms in the literature; it can be extended to any number of mixture components and any number of vector coordinates of the multivariate observations. Thus it may be applied even in situations where the model is not identifiable, so care is called for when using it in situations for which identifiability is difficult to establish conclusively. Our algorithm yields much smaller mean integrated squared errors than an alternative algorithm in a simulation study. In another example using a real dataset, it provides new insights that extend previous analyses. Finally, we present two different variations of our algorithm, one stochastic and one deterministic, and find anecdotal evidence that there is not a great deal of difference between the performance of these two variants. The computer code and data used in this article are available online.
ISSN:1061-8600
1537-2715
DOI:10.1198/jcgs.2009.07175