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Maximum smoothed likelihood for multivariate mixtures


  • M. Levine
  • D. R. Hunter
  • D. Chauveau


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. Copyright 2011, Oxford University Press.

Suggested Citation

  • M. Levine & D. R. Hunter & D. Chauveau, 2011. "Maximum smoothed likelihood for multivariate mixtures," Biometrika, Biometrika Trust, vol. 98(2), pages 403-416.
  • Handle: RePEc:oup:biomet:v:98:y:2011:i:2:p:403-416

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    Cited by:

    1. Jean-Marc Robin & Stéphane Bonhomme & Koen Jochmans, 2014. "Estimating Multivariate Latent-Structure Models," Sciences Po Economics Discussion Papers 2014-18, Sciences Po Departement of Economics.
    2. repec:eee:econom:v:201:y:2017:i:2:p:237-248 is not listed on IDEAS
    3. Stéphane Bonhomme & Koen Jochmans & Jean-Marc Robin, 2016. "Non-parametric estimation of finite mixtures from repeated measurements," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(1), pages 211-229, January.
    4. Stéphane Bonhomme & Koen Jochmans & Jean-Marc Robin, 2014. "Nonparametric spectral-based estimation of latent structures," CeMMAP working papers CWP18/14, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    5. Chauveau, Didier & Hoang, Vy Thuy Lynh, 2016. "Nonparametric mixture models with conditionally independent multivariate component densities," Computational Statistics & Data Analysis, Elsevier, vol. 103(C), pages 1-16.
    6. Hiroyuki Kasahara & Katsumi Shimotsu, 2014. "Non-parametric identification and estimation of the number of components in multivariate mixtures," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 76(1), pages 97-111, January.
    7. Bonhomme, Stéphane & Jochmans, Koen & Robin, Jean-Marc, 2017. "Nonparametric estimation of non-exchangeable latent-variable models," Journal of Econometrics, Elsevier, vol. 201(2), pages 237-248.
    8. Stéphane Bonhomme & Koen Jochmans & Jean-Marc Robin, 2017. "Nonparametric estimation of non-exchangeable latent-variable models," Sciences Po publications info:hdl:2441/4m4fqk908d9, Sciences Po.
    9. David Balan & Patrick DeGraba & Francine Lafontaine & Patrick McAlvanah & Devesh Raval & David Schmidt, 2015. "Economics at the FTC: Fraud, Mergers and Exclusion," Review of Industrial Organization, Springer;The Industrial Organization Society, vol. 47(4), pages 371-398, December.
    10. repec:spr:jclass:v:34:y:2017:i:3:d:10.1007_s00357-017-9243-9 is not listed on IDEAS

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