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Posterior Consistency In Conditional Density Estimation By Covariate Dependent Mixtures

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  • Norets, Andriy
  • Pelenis, Justinas

Abstract

This paper considers Bayesian nonparametric estimation of conditional densities by countable mixtures of location-scale densities with covariate dependent mixing probabilities. The mixing probabilities are modeled in two ways. First, we consider finite covariate dependent mixture models, in which the mixing probabilities are proportional to a product of a constant and a kernel and a prior on the number of mixture components is specified. Second, we consider kernel stick-breaking processes for modeling the mixing probabilities. We show that the posterior in these two models is weakly and strongly consistent for a large class of data-generating processes. A simulation study conducted in the paper demonstrates that the models can perform well in small samples.

Suggested Citation

  • Norets, Andriy & Pelenis, Justinas, 2014. "Posterior Consistency In Conditional Density Estimation By Covariate Dependent Mixtures," Econometric Theory, Cambridge University Press, vol. 30(3), pages 606-646, June.
    • Handle: RePEc:cup:etheor:v:30:y:2014:i:03:p:606-646_00
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    Cited by:

    1. Hien Duy Nguyen & TrungTin Nguyen & Faicel Chamroukhi & Geoffrey John McLachlan, 2021. "Approximations of conditional probability density functions in Lebesgue spaces via mixture of experts models," Journal of Statistical Distributions and Applications, Springer, vol. 8(1), pages 1-15, December.
    2. Taisuke Nakata & Christopher Tonetti, 2015. "Small Sample Properties of Bayesian Estimators of Labor Income Processes," Journal of Applied Economics, Taylor & Francis Journals, vol. 18(1), pages 121-148, May.
    3. Pelenis, Justinas, 2012. "Bayesian Semiparametric Regression," Economics Series 285, Institute for Advanced Studies.
    4. Norets, Andriy & Pelenis, Justinas, 2022. "Adaptive Bayesian estimation of conditional discrete-continuous distributions with an application to stock market trading activity," Journal of Econometrics, Elsevier, vol. 230(1), pages 62-82.
    5. Barrientos, Andrés F. & Canale, Antonio, 2021. "A Bayesian goodness-of-fit test for regression," Computational Statistics & Data Analysis, Elsevier, vol. 155(C).
    6. A. R. Linero, 2017. "Bayesian nonparametric analysis of longitudinal studies in the presence of informative missingness," Biometrika, Biometrika Trust, vol. 104(2), pages 327-341.
    7. Federico Bassetti & Roberto Casarin & Francesco Ravazzolo, 2018. "Bayesian Nonparametric Calibration and Combination of Predictive Distributions," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(522), pages 675-685, April.
    8. Villani, Mattias & Kohn, Robert & Nott, David J., 2012. "Generalized smooth finite mixtures," Journal of Econometrics, Elsevier, vol. 171(2), pages 121-133.
    9. Norets, Andriy, 2015. "Bayesian regression with nonparametric heteroskedasticity," Journal of Econometrics, Elsevier, vol. 185(2), pages 409-419.
    10. Debdeep Pati & David Dunson, 2014. "Bayesian nonparametric regression with varying residual density," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(1), pages 1-31, February.
    11. Norets, Andriy & Pelenis, Justinas, 2012. "Bayesian modeling of joint and conditional distributions," Journal of Econometrics, Elsevier, vol. 168(2), pages 332-346.

    More about this item

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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