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Nonparametric spectral-based estimation of latent structures

Author

Listed:
  • Stéphane Bonhomme

    (Institute for Fiscal Studies and University of Chicago)

  • Koen Jochmans

    (Institute for Fiscal Studies and University of Cambridge)

  • Jean-Marc Robin

    (Institute for Fiscal Studies and Sciences Po and University College London)

Abstract

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.

Suggested Citation

  • 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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    File URL: https://www.cemmap.ac.uk/wps/cwp181414.pdf
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    References listed on IDEAS

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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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