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Asymptotic properties of nonparametric estimation and quantile regression in Bayesian structural equation models

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  • Kim, Gwangsu
  • Choi, Taeryon

Abstract

We study the asymptotic properties of nonparametric Bayesian structural equation models (SEMs). Under mild conditions, when adjusting nonparametric error distributions, the posteriors of Bayesian SEMs achieve the optimal convergence rate up to logn terms in the nonparametric means and nonlinear relationships of the latent variables. Furthermore, we consider quantile regressions of the error and latent variables in Bayesian SEMs, and we show posterior consistency in Bayesian quantile regression. The theoretical results are validated using simulation studies.

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  • Kim, Gwangsu & Choi, Taeryon, 2019. "Asymptotic properties of nonparametric estimation and quantile regression in Bayesian structural equation models," Journal of Multivariate Analysis, Elsevier, vol. 171(C), pages 68-82.
    • Handle: RePEc:eee:jmvana:v:171:y:2019:i:c:p:68-82
    DOI: 10.1016/j.jmva.2018.11.009
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    References listed on IDEAS

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    1. Neumeyer, N. & Van Keilegom, I., 2010. "Estimating the error distribution in nonparametric multiple regression with applications to model testing," LIDAM Reprints ISBA 2010006, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    2. Choi, Taeryon & Schervish, Mark J., 2007. "On posterior consistency in nonparametric regression problems," Journal of Multivariate Analysis, Elsevier, vol. 98(10), pages 1969-1987, November.
    3. Umbach, Nora & Naumann, Katharina & Brandt, Holger & Kelava, Augustin, 2017. "Fitting Nonlinear Structural Equation Models in R with Package nlsem," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 77(i07).
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    7. Feng, Xiang-Nan & Wang, Yifan & Lu, Bin & Song, Xin-Yuan, 2017. "Bayesian regularized quantile structural equation models," Journal of Multivariate Analysis, Elsevier, vol. 154(C), pages 234-248.
    8. Mingan Yang & David Dunson, 2010. "Bayesian Semiparametric Structural Equation Models with Latent Variables," Psychometrika, Springer;The Psychometric Society, vol. 75(4), pages 675-693, December.
    9. Neumeyer, Natalie & Van Keilegom, Ingrid, 2010. "Estimating the error distribution in nonparametric multiple regression with applications to model testing," Journal of Multivariate Analysis, Elsevier, vol. 101(5), pages 1067-1078, May.
    10. Gwangsu Kim & Yongdai Kim & Taeryon Choi, 2017. "Bayesian Analysis of the Proportional Hazards Model with Time-Varying Coefficients," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(2), pages 524-544, June.
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