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Nonparametric spectral-based estimation of latent structures


  • Stéphane Bonhomme

    () (Institute for Fiscal Studies and University of Chicago)

  • Koen Jochmans

    (Institute for Fiscal Studies and Sciences Po)

  • Jean-Marc Robin

    () (Institute for Fiscal Studies and cemmap and Sciences Po)


We present a constructive identification proof of p-linear decompositions of q-way arrays. The analysis is based on the joint spectral decomposition of a set of matrices. It has applications in the analysis of a variety of latent-structure models, such as q-variate mixtures of p distributions. As such, our results provide a constructive alternative to Allman, Matias and Rhodes [2009]. The identification argument suggests a joint approximate-diagonalization estimator that is easy to implement and whose asymptotic properties we derive. We illustrate the usefulness of our approach by applying it to nonparametrically estimate multivariate finite-mixture models and hidden Markov models.

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  • 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.
  • Handle: RePEc:ifs:cemmap:18/14

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    References listed on IDEAS

    1. T. Anderson, 1954. "On estimation of parameters in latent structure analysis," Psychometrika, Springer;The Psychometric Society, vol. 19(1), pages 1-10, March.
    2. Stéphane Bonhomme & Koen Jochmans & Jean-Marc Robin, 2013. "Nonparametric estimation of finite mixtures," Sciences Po Economics Discussion Papers 2013-09, Sciences Po Departement of Economics.
    3. M. Levine & D. R. Hunter & D. Chauveau, 2011. "Maximum smoothed likelihood for multivariate mixtures," Biometrika, Biometrika Trust, vol. 98(2), pages 403-416.
    4. Marc Henry & Koen Jochmans & Bernard Salanié, 2014. "Inference on Mixtures Under Tail Restrictions," Working Papers hal-01053810, HAL.
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    6. Bert Green, 1951. "A general solution for the latent class model of latent structure analysis," Psychometrika, Springer;The Psychometric Society, vol. 16(2), pages 151-166, June.
    7. Peter Hall & Amnon Neeman & Reza Pakyari & Ryan Elmore, 2005. "Nonparametric inference in multivariate mixtures," Biometrika, Biometrika Trust, vol. 92(3), pages 667-678, September.
    8. Hu, Yingyao, 2008. "Identification and estimation of nonlinear models with misclassification error using instrumental variables: A general solution," Journal of Econometrics, Elsevier, vol. 144(1), pages 27-61, May.
    9. Magnus, Jan R., 1985. "On Differentiating Eigenvalues and Eigenvectors," Econometric Theory, Cambridge University Press, vol. 1(02), pages 179-191, August.
    10. Magnus, J.R., 1985. "On differentiating eigenvalues and eigenvectors," Other publications TiSEM f410e3a5-ba9b-4787-b8cc-4, Tilburg University, School of Economics and Management.
    11. Joseph Kruskal, 1976. "More factors than subjects, tests and treatments: An indeterminacy theorem for canonical decomposition and individual differences scaling," Psychometrika, Springer;The Psychometric Society, vol. 41(3), pages 281-293, September.
    12. Hiroyuki Kasahara & Katsumi Shimotsu, 2009. "Nonparametric Identification of Finite Mixture Models of Dynamic Discrete Choices," Econometrica, Econometric Society, vol. 77(1), pages 135-175, January.
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