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Nonparametric estimation of a latent variable model

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  • Kelava, Augustin
  • Kohler, Michael
  • Krzyżak, Adam
  • Schaffland, Tim Fabian

Abstract

In this paper a nonparametric latent variable model is estimated without specifying the underlying distributions. The main idea is to estimate in a first step a common factor analysis model under the assumption that each manifest variable is influenced by at most one of the latent variables. In a second step nonparametric regression is used to analyze the relation between the latent variables. Theoretical results concerning consistency of the estimates are presented, and the finite sample size performance of the estimates is illustrated by applying them to simulated data.

Suggested Citation

  • Kelava, Augustin & Kohler, Michael & Krzyżak, Adam & Schaffland, Tim Fabian, 2017. "Nonparametric estimation of a latent variable model," Journal of Multivariate Analysis, Elsevier, vol. 154(C), pages 112-134.
    • Handle: RePEc:eee:jmvana:v:154:y:2017:i:c:p:112-134
    DOI: 10.1016/j.jmva.2016.10.006
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    References listed on IDEAS

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    1. Jushan Bai & Serena Ng, 2002. "Determining the Number of Factors in Approximate Factor Models," Econometrica, Econometric Society, vol. 70(1), pages 191-221, January.
    2. C. Vale & Vincent Maurelli, 1983. "Simulating multivariate nonnormal distributions," Psychometrika, Springer;The Psychometric Society, vol. 48(3), pages 465-471, September.
    3. Zhao, L. C., 1987. "Exponential bounds of mean error for the nearest neighbor estimates of regression functions," Journal of Multivariate Analysis, Elsevier, vol. 21(1), pages 168-178, February.
    4. Irina Irincheeva & Eva Cantoni & Marc G. Genton, 2012. "Generalized Linear Latent Variable Models with Flexible Distribution of Latent Variables," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 39(4), pages 663-680, December.
    5. Breslaw, Jon A. & McIntosh, James, 1998. "Simulated latent variable estimation of models with ordered categorical data," Journal of Econometrics, Elsevier, vol. 87(1), pages 25-47, August.
    6. Andreas Klein & Helfried Moosbrugger, 2000. "Maximum likelihood estimation of latent interaction effects with the LMS method," Psychometrika, Springer;The Psychometric Society, vol. 65(4), pages 457-474, December.
    7. Peter Hall & Hans‐Georg Müller & Fang Yao, 2008. "Modelling sparse generalized longitudinal observations with latent Gaussian processes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(4), pages 703-723, September.
    8. Francesco Bartolucci, 2006. "Likelihood inference for a class of latent Markov models under linear hypotheses on the transition probabilities," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(2), pages 155-178, April.
    9. Conne, David & Ronchetti, Elvezio & Victoria-Feser, Maria-Pia, 2010. "Goodness of Fit for Generalized Linear Latent Variables Models," Journal of the American Statistical Association, American Statistical Association, vol. 105(491), pages 1126-1134.
    10. R. Jennrich & P. Sampson, 1966. "Rotation for simple loadings," Psychometrika, Springer;The Psychometric Society, vol. 31(3), pages 313-323, September.
    11. Anderson, T. W., 1989. "Linear latent variable models and covariance structures," Journal of Econometrics, Elsevier, vol. 41(1), pages 91-119, May.
    12. Bai, Jushan & Ng, Serena, 2006. "Evaluating latent and observed factors in macroeconomics and finance," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 507-537.
    13. Francesco Bartolucci & Fulvia Pennoni & Brian Francis, 2007. "A latent Markov model for detecting patterns of criminal activity," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 170(1), pages 115-132, January.
    14. 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.
    15. Li, Tong, 2002. "Robust and consistent estimation of nonlinear errors-in-variables models," Journal of Econometrics, Elsevier, vol. 110(1), pages 1-26, September.
    16. Bianconcini, Silvia & Cagnone, Silvia, 2012. "Estimation of generalized linear latent variable models via fully exponential Laplace approximation," Journal of Multivariate Analysis, Elsevier, vol. 112(C), pages 183-193.
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