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Maximum smoothed likelihood for multivariate mixtures

Author

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

Abstract

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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    File URL: http://hdl.handle.net/10.1093/biomet/asq079
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    Citations

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    Cited by:

    1. 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.
    2. Stéphane Bonhomme & Koen Jochmans & Jean-Marc Robin, 2014. "Estimating Multivariate Latent-Structure Models," Working Papers hal-01097135, HAL.
    3. Stéphane Bonhomme & Koen Jochmans & Jean-Marc Robin, 2014. "Nonparametric spectral-based estimation of latent structures," CeMMAP working papers 18/14, Institute for Fiscal Studies.
    4. Hema Yoganarasimhan, 2016. "Estimation of Beauty Contest Auctions," Marketing Science, INFORMS, vol. 35(1), pages 27-54, January.
    5. 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.
    6. 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.
    7. 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.
    8. Mazo, Gildas & Averyanov, Yaroslav, 2019. "Constraining kernel estimators in semiparametric copula mixture models," Computational Statistics & Data Analysis, Elsevier, vol. 138(C), pages 170-189.
    9. 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.
    10. 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.
    11. Xiaotian Zhu & David R. Hunter, 2019. "Clustering via finite nonparametric ICA mixture models," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 13(1), pages 65-87, March.
    12. Gildas Mazo, 2017. "A Semiparametric and Location-Shift Copula-Based Mixture Model," Journal of Classification, Springer;The Classification Society, vol. 34(3), pages 444-464, October.
    13. Yanyuan Ma & Shaoli Wang & Lin Xu & Weixin Yao, 2021. "Semiparametric mixture regression with unspecified error distributions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(2), pages 429-444, June.
    14. repec:hal:spmain:info:hdl:2441/etefo8s8r89oamhnhiclqr530 is not listed on IDEAS
    15. Konstantin T. Matchev & Prasanth Shyamsundar, 2020. "InClass Nets: Independent Classifier Networks for Nonparametric Estimation of Conditional Independence Mixture Models and Unsupervised Classification," Papers 2009.00131, arXiv.org.
    16. Paul Schrimpf & Michio Suzuki & Hiroyuki Kasahara, 2015. "Identification and Estimation of Production Function with Unobserved Heterogeneity," 2015 Meeting Papers 924, Society for Economic Dynamics.
    17. repec:spo:wpmain:info:hdl:2441/etefo8s8r89oamhnhiclqr530 is not listed on IDEAS
    18. David Hunter & Derek Young, 2012. "Semiparametric mixtures of regressions," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(1), pages 19-38.
    19. Jiali Zheng & Xiyang Wang, 2022. "Estimation for a Class of Semiparametric Pareto Mixture Densities," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(2), pages 609-627, August.
    20. repec:hal:spmain:info:hdl:2441/lpag9391598uoauqu4u9opq76 is not listed on IDEAS
    21. 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.
    22. repec:hal:spmain:info:hdl:2441/4m4fqk908d9obqasu0uhft7t94 is not listed on IDEAS
    23. Xiaotian Zhu & David R. Hunter, 2016. "Theoretical grounding for estimation in conditional independence multivariate finite mixture models," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 28(4), pages 683-701, October.
    24. 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.

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