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Maximum smoothed likelihood for multivariate mixtures. (English) Zbl 1215.62055
Summary: We introduce an algorithm for estimating the parameters in a finite mixture of completely unspecified multivariate components in at least three dimensions under the assumption of conditionally independent coordinate dimensions. We prove that this algorithm, based on a majorization-minimization idea, possesses a desirable descent property just as any EM algorithm does. We discuss the similarities between our algorithm and a related one, the so-called nonlinearly smoothed EM algorithm for the non-mixture setting. We also demonstrate via simulation studies that the new algorithm gives very similar results to another algorithm that has been shown empirically to be effective but that does not satisfy any descent property. We provide code for implementing the new algorithm in a publicly available R package.

MSC:
62H12 Estimation in multivariate analysis
62G05 Nonparametric estimation
65C60 Computational problems in statistics (MSC2010)
Software:
R; mixtools
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