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Posterior Consistency in Conditional Density Estimation by Covariate Dependent Mixtures

Author

Listed:
  • Norets, Andriy

    (Department of Economics, Princeton University, Princeton, USA)

  • Pelenis, Justinas

    (Department of Economics and Finance, Institute for Advanced Studies, Vienna, Austria)

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.

Suggested Citation

  • Norets, Andriy & Pelenis, Justinas, 2011. "Posterior Consistency in Conditional Density Estimation by Covariate Dependent Mixtures," Economics Series 282, Institute for Advanced Studies.
    • Handle: RePEc:ihs:ihsesp:282
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    File URL: https://irihs.ihs.ac.at/id/eprint/2108
    File Function: First version, 2011
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    Cited by:

    1. Taisuke Nakata & Christopher Tonetti, 2015. "Small sample properties of Bayesian estimators of labor income processes," Journal of Applied Economics, Universidad del CEMA, vol. 18, pages 121-148, May.
    2. 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.
    3. Barrientos, Andrés F. & Canale, Antonio, 2021. "A Bayesian goodness-of-fit test for regression," Computational Statistics & Data Analysis, Elsevier, vol. 155(C).
    4. Villani, Mattias & Kohn, Robert & Nott, David J., 2012. "Generalized smooth finite mixtures," Journal of Econometrics, Elsevier, vol. 171(2), pages 121-133.
    5. 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.
    6. 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.
    7. Pelenis, Justinas, 2012. "Bayesian Semiparametric Regression," Economics Series 285, Institute for Advanced Studies.
    8. 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.
    9. Norets, Andriy, 2015. "Bayesian regression with nonparametric heteroskedasticity," Journal of Econometrics, Elsevier, vol. 185(2), pages 409-419.
    10. Norets, Andriy & Pelenis, Justinas, 2012. "Bayesian modeling of joint and conditional distributions," Journal of Econometrics, Elsevier, vol. 168(2), pages 332-346.
    11. 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.

    More about this item

    Keywords

    Bayesian nonparametrics; posterior consistency; conditional density estimation; mixtures of normal distributions; location-scale mixtures; smoothly mixing regressions; mixtures of experts; dependent Dirichlet process; kernel stick-breaking process;
    All these keywords.

    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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