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Posterior Consistency in Conditional Density Estimation by Covariate Dependent Mixtures

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  • 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.

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File URL: http://www.ihs.ac.at/publications/eco/es-282.pdf
File Function: First version, 2011
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Bibliographic Info

Paper provided by Institute for Advanced Studies in its series Economics Series with number 282.

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Length: 26 pages
Date of creation: Dec 2011
Date of revision:
Handle: RePEc:ihs:ihsesp:282

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Related research

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;

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Cited by:
  1. Norets, Andriy & Pelenis, Justinas, 2012. "Bayesian modeling of joint and conditional distributions," Journal of Econometrics, Elsevier, vol. 168(2), pages 332-346.
  2. Debdeep Pati & David Dunson, 2014. "Bayesian nonparametric regression with varying residual density," Annals of the Institute of Statistical Mathematics, Springer, vol. 66(1), pages 1-31, February.
  3. Pelenis, Justinas, 2012. "Bayesian Semiparametric Regression," Economics Series 285, Institute for Advanced Studies.
  4. Villani, Mattias & Kohn, Robert & Nott, David J., 2012. "Generalized smooth finite mixtures," Journal of Econometrics, Elsevier, vol. 171(2), pages 121-133.

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