Maximum Smoothed Likelihood for Multivariate Mixtures

Michael Levine (1) , David R. Hunter (2) , Didier Chauveau (3)

1 Department of Statistics [West Lafayette]
2 Department of Statistics, Penn State University
3 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans

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, or NEMS, algorithm for the non-mixture setting. We also demonstrate via simulation studies that the new algorithm gives very similar results to another algorithm that does not satisfy any descent algorithm, thus validating the latter algorithm, which can be simpler to program. We provide code for implementing the new algorithm in a publicly-available R package.

Mots clés: EM algorithms; MM algorithms; NEMS; nonparametric mixtures

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Michael Levine, David R. Hunter, Didier Chauveau. Maximum Smoothed Likelihood for Multivariate Mixtures. Biometrika, 2011, 98 (2), pp.403-416. ⟨10.1093/biomet/asq079⟩. ⟨hal-00516391⟩