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Bayesian modeling of joint and conditional distributions

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  • Norets, Andriy
  • Pelenis, Justinas

Abstract

In this paper, we study a Bayesian approach to flexible modeling of conditional distributions. The approach uses a flexible model for the joint distribution of the dependent and independent variables and then extracts the conditional distributions of interest from the estimated joint distribution. We use a finite mixture of multivariate normals (FMMN) to estimate the joint distribution. The conditional distributions can then be assessed analytically or through simulations. The discrete variables are handled through the use of latent variables. The estimation procedure employs an MCMC algorithm. We provide a characterization of the Kullback–Leibler closure of FMMN and show that the joint and conditional predictive densities implied by the FMMN model are consistent estimators for a large class of data generating processes with continuous and discrete observables. The method can be used as a robust regression model with discrete and continuous dependent and independent variables and as a Bayesian alternative to semi- and non-parametric models such as quantile and kernel regression. In experiments, the method compares favorably with classical nonparametric and alternative Bayesian methods.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 168 (2012)
Issue (Month): 2 ()
Pages: 332-346

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Handle: RePEc:eee:econom:v:168:y:2012:i:2:p:332-346

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Web page: http://www.elsevier.com/locate/jeconom

Related research

Keywords: Mixture of normal distributions; Consistency; Bayesian conditional density estimation; Heteroscedasticity and non-linearity robust inference;

References

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  1. De Iorio, Maria & Muller, Peter & Rosner, Gary L. & MacEachern, Steven N., 2004. "An ANOVA Model for Dependent Random Measures," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 205-215, January.
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Citations

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Cited by:
  1. Sam Schulhofer-Wohl & Andriy Norets, 2009. "Heterogeneity in income processes," 2009 Meeting Papers 999, Society for Economic Dynamics.
  2. Pelenis, Justinas, 2014. "Bayesian regression with heteroscedastic error density and parametric mean function," Journal of Econometrics, Elsevier, vol. 178(P3), pages 624-638.

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