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Non-parametric estimation of finite mixtures from repeated measurements

Author

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  • Stéphane Bonhomme
  • Koen Jochmans
  • Jean-Marc Robin

Abstract

This paper provides methods to estimate finite mixtures from data with repeated measurements non-parametrically. We present a constructive identification argument and use it to develop simple two-step estimators of the component distributions and all their functionals. We discuss a computationally efficient method for estimation and derive asymptotic theory. Simulation experiments suggest that our theory provides confidence intervals with good coverage in small samples.
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Suggested Citation

  • 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.
    • Handle: RePEc:bla:jorssb:v:78:y:2016:i:1:p:211-229
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    1. 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.
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    Citations

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    Cited by:

    1. Jochmans, Koen & Henry, Marc & Salanié, Bernard, 2017. "Inference On Two-Component Mixtures Under Tail Restrictions," Econometric Theory, Cambridge University Press, vol. 33(3), pages 610-635, June.
    2. 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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    4. Koen Jochmans & Martin Weidner, 2018. "Inference on a Distribution from Noisy Draws," Papers 1803.04991, arXiv.org, revised Dec 2021.
    5. Charles Bellemare & Alexander Sebald, 2019. "Measuring Belief-Dependent Preferences without Information about Beliefs," CESifo Working Paper Series 7505, CESifo.
    6. Rasmus Lentz & Suphanit Piyapromdee & Jean-Marc Robin, 2018. "On Worker and Firm Heterogeneity in Wages and Employment Mobility: Evidence from Danish Register Data," PIER Discussion Papers 91, Puey Ungphakorn Institute for Economic Research.
    7. Hu, Yingyao, 2017. "The econometrics of unobservables: Applications of measurement error models in empirical industrial organization and labor economics," Journal of Econometrics, Elsevier, vol. 200(2), pages 154-168.
    8. Stephane Bonhomme, 2021. "Teams: Heterogeneity, Sorting, and Complementarity," Papers 2102.01802, arXiv.org.
    9. Qihui Chen & Zheng Fang, 2018. "Improved Inference on the Rank of a Matrix," Papers 1812.02337, arXiv.org, revised Mar 2019.
    10. Engel, Christoph, 2020. "Estimating heterogeneous reactions to experimental treatments," Journal of Economic Behavior & Organization, Elsevier, vol. 178(C), pages 124-147.
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    12. 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.
    13. 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.
    14. Krasnokutskaya, Elena & Song, Kyungchul & Tang, Xun, 2022. "Estimating unobserved individual heterogeneity using pairwise comparisons," Journal of Econometrics, Elsevier, vol. 226(2), pages 477-497.
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