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Nonparametric Regression Density Estimation Using Smoothly Varying Normal Mixtures

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Author Info

  • Villani, Mattias

    ()
    (Research Department, Central Bank of Sweden)

  • Kohn, Robert

    ()
    (Faculty of Business, University of New South Wales)

  • Giordani, Paolo

    ()
    (Research Department, Central Bank of Sweden)

Abstract

We model a regression density nonparametrically so that at each value of the covariates the density is a mixture of normals with the means, variances and mixture probabilities of the com- ponents changing smoothly as a function of the covariates. The model extends existing models in two important ways. First, the components are allowed to be heteroscedastic regressions as the standard model with homoscedastic regressions can give a poor fit to heteroscedastic data, especially when the number of covariates is large. Furthermore, we typically need a lot fewer heteroscedastic components, which makes it easier to interpret the model and speeds up the computation. The second main extension is to introduce a novel variable selection prior into all the components of the model. The variable selection prior acts as a self-adjusting mech- anism that prevents overfitting and makes it feasible to fit high-dimensional nonparametric surfaces. We use Bayesian inference and Markov Chain Monte Carlo methods to estimate the model. Simulated and real examples are used to show that the full generality of our model is required to fit a large class of densities.

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Bibliographic Info

Paper provided by Sveriges Riksbank (Central Bank of Sweden) in its series Working Paper Series with number 211.

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Length: 46 pages
Date of creation: 01 Sep 2007
Date of revision:
Handle: RePEc:hhs:rbnkwp:0211

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Postal: Sveriges Riksbank, SE-103 37 Stockholm, Sweden
Phone: 08 - 787 00 00
Fax: 08-21 05 31
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Web page: http://www.riksbank.com/
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Related research

Keywords: Bayesian inference; Markov Chain Monte Carlo; Mixture of Experts; Predictive inference; Splines; Value-at-Risk; Variable selection;

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References

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  1. 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.
  2. Smith, Michael & Kohn, Robert, 1996. "Nonparametric regression using Bayesian variable selection," Journal of Econometrics, Elsevier, vol. 75(2), pages 317-343, December.
  3. David J. Nott & Robert Kohn, 2005. "Adaptive sampling for Bayesian variable selection," Biometrika, Biometrika Trust, vol. 92(4), pages 747-763, December.
  4. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521785167, December.
  5. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521780506, December.
  6. Geweke, John & Keane, Michael, 2007. "Smoothly mixing regressions," Journal of Econometrics, Elsevier, vol. 138(1), pages 252-290, May.
  7. Geweke, John, 2007. "Interpretation and inference in mixture models: Simple MCMC works," Computational Statistics & Data Analysis, Elsevier, vol. 51(7), pages 3529-3550, April.
  8. 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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Cited by:
  1. 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.
  2. Chib, Siddhartha & Greenberg, Edward, 2010. "Additive cubic spline regression with Dirichlet process mixture errors," Journal of Econometrics, Elsevier, vol. 156(2), pages 322-336, June.

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