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

Tatiana Benaglia, Didier Chauveau and David R. Hunter
Journal of Computational and Graphical Statistics
Vol. 18, No. 2 (June 2009), pp. 505-526
Stable URL: http://www.jstor.org/stable/25651257
Page Count: 22
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An EM-Like Algorithm for Semi- and Nonparametric Estimation in Multivariate Mixtures
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Abstract

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.

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