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Generalized smooth finite mixtures

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  • Villani, Mattias
  • Kohn, Robert
  • Nott, David J.

Abstract

We propose a general class of models and a unified Bayesian inference methodology for flexibly estimating the density of a response variable conditional on a possibly high-dimensional set of covariates. Our model is a finite mixture of component models with covariate-dependent mixing weights. The component densities can belong to any parametric family, with each model parameter being a deterministic function of covariates through a link function. Our MCMC methodology allows for Bayesian variable selection among the covariates in the mixture components and in the mixing weights. The model’s parameterization and variable selection prior are chosen to prevent overfitting. We use simulated and real data sets to illustrate the methodology.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 171 (2012)
Issue (Month): 2 ()
Pages: 121-133

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Handle: RePEc:eee:econom:v:171:y:2012:i:2:p:121-133

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

Related research

Keywords: Bayesian inference; Conditional distribution; GLM; Markov chain Monte Carlo; Mixture of experts; Variable selection;

References

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  1. John Geweke, 1998. "Using simulation methods for Bayesian econometric models: inference, development, and communication," Staff Report 249, Federal Reserve Bank of Minneapolis.
  2. Joao A. Bastos & Joaquim J. S. Ramalho, 2010. "Nonparametric models of financial leverage decisions," CEMAPRE Working Papers 1005, Centre for Applied Mathematics and Economics (CEMAPRE), School of Economics and Management (ISEG), Technical University of Lisbon.
  3. David B. Dunson & Natesh Pillai & Ju-Hyun Park, 2007. "Bayesian density regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(2), pages 163-183.
  4. Peter J. Green, 2001. "Modelling Heterogeneity With and Without the Dirichlet Process," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics & Finnish Statistical Society & Norwegian Statistical Association & Swedish Statistical Association, vol. 28(2), pages 355-375.
  5. Esmeralda A. Ramalho & Joaquim J.S. Ramalho & José M.R. Murteira, 2009. "Alternative estimating and testing empirical strategies for fractional regression models," CEFAGE-UE Working Papers 2009_08, University of Evora, CEFAGE-UE (Portugal).
  6. Cook, Douglas O. & Kieschnick, Robert & McCullough, B.D., 2008. "Regression analysis of proportions in finance with self selection," Journal of Empirical Finance, Elsevier, vol. 15(5), pages 860-867, December.
  7. Rajan, Raghuram G & Zingales, Luigi, 1995. " What Do We Know about Capital Structure? Some Evidence from International Data," Journal of Finance, American Finance Association, vol. 50(5), pages 1421-60, December.
  8. Geweke, John & Keane, Michael, 2007. "Smoothly mixing regressions," Journal of Econometrics, Elsevier, vol. 138(1), pages 252-290, May.
  9. Norets, Andriy & Pelenis, Justinas, 2011. "Posterior Consistency in Conditional Density Estimation by Covariate Dependent Mixtures," Economics Series 282, Institute for Advanced Studies.
  10. Wayne DeSarbo & William Cron, 1988. "A maximum likelihood methodology for clusterwise linear regression," Journal of Classification, Springer, vol. 5(2), pages 249-282, September.
  11. Giordani, Paolo & Jacobson, Tor & von Schedvin , Erik & Villani, Mattias, 2011. "Taking the Twists into Account: Predicting Firm Bankruptcy Risk with Splines of Financial Ratios," Working Paper Series 256, Sveriges Riksbank (Central Bank of Sweden).
  12. Chung, Yeonseung & Dunson, David B., 2009. "Nonparametric Bayes Conditional Distribution Modeling With Variable Selection," Journal of the American Statistical Association, American Statistical Association, vol. 104(488), pages 1646-1660.
  13. Villani, Mattias & Kohn, Robert & Giordani, Paolo, 2009. "Regression density estimation using smooth adaptive Gaussian mixtures," Journal of Econometrics, Elsevier, vol. 153(2), pages 155-173, December.
  14. Andreas Million & Regina T. Riphahn & Achim Wambach, 2003. "Incentive effects in the demand for health care: a bivariate panel count data estimation," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 18(4), pages 387-405.
  15. David J. Nott & Robert Kohn, 2005. "Adaptive sampling for Bayesian variable selection," Biometrika, Biometrika Trust, vol. 92(4), pages 747-763, December.
  16. Sally A. Wood, 2002. "Bayesian mixture of splines for spatially adaptive nonparametric regression," Biometrika, Biometrika Trust, vol. 89(3), pages 513-528, August.
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Cited by:
  1. Quiroz, Matias & Villani, Mattias, 2013. "Dynamic mixture-of-experts models for longitudinal and discrete-time survival data," Working Paper Series 268, Sveriges Riksbank (Central Bank of Sweden).

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