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Posterior Consistency in Conditional Density Estimation by Covariate Dependent Mixtures


  • Norets, Andriy

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

  • Pelenis, Justinas

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


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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    References listed on IDEAS

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    5. Osili, Una Okonkwo & Long, Bridget Terry, 2008. "Does female schooling reduce fertility? Evidence from Nigeria," Journal of Development Economics, Elsevier, vol. 87(1), pages 57-75, August.
    6. repec:pri:cheawb:adriana_booms.pdf is not listed on IDEAS
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    9. Janet Currie & Enrico Moretti, 2003. "Mother's Education and the Intergenerational Transmission of Human Capital: Evidence from College Openings," The Quarterly Journal of Economics, Oxford University Press, vol. 118(4), pages 1495-1532.
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    Cited by:

    1. Pelenis, Justinas, 2012. "Bayesian Semiparametric Regression," Economics Series 285, Institute for Advanced Studies.
    2. repec:oup:biomet:v:104:y:2017:i:2:p:327-341. is not listed on IDEAS
    3. Roberto Casarin & Federico Bassetti & Francesco Ravazzolo, 2015. "Bayesian Nonparametric Calibration and Combination of Predictive Distributions," Working Papers 2015:04, Department of Economics, University of Venice "Ca' Foscari".
    4. Norets, Andriy, 2015. "Bayesian regression with nonparametric heteroskedasticity," Journal of Econometrics, Elsevier, vol. 185(2), pages 409-419.
    5. Norets, Andriy & Pelenis, Justinas, 2012. "Bayesian modeling of joint and conditional distributions," Journal of Econometrics, Elsevier, vol. 168(2), pages 332-346.
    6. 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.
    7. Villani, Mattias & Kohn, Robert & Nott, David J., 2012. "Generalized smooth finite mixtures," Journal of Econometrics, Elsevier, vol. 171(2), pages 121-133.
    8. 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.

    More about this item


    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;

    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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