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Bayesian Regression Analysis With Scale Mixtures Of Normals

  • Fern ndez, Carmen
  • Steel, Mark F.J.

This paper considers a Bayesian analysis of the linear regression model under independent sampling from general scale mixtures of Normals. Using a common reference prior, we investigate the validity of Bayesian inference and the existence of posterior moments of the regression and scale parameters. We find that whereas existence of the posterior distribution does not depend on the choice of the design matrix or the mixing distribution, both of them can crucially intervene in the existence of posterior moments. We identify some useful characteristics that allow for an easy verification of the existence of a wide range of moments. In addition, we provide full characterizations under sampling from finite mixtures of Normals, Pearson VII or certain Modulated Normal distributions. For empirical applications, a numerical implementation based on the Gibbs sampler is recommended.

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Article provided by Cambridge University Press in its journal Econometric Theory.

Volume (Year): 16 (2000)
Issue (Month): 01 (February)
Pages: 80-101

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Handle: RePEc:cup:etheor:v:16:y:2000:i:01:p:80-101_16
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  1. Eric Jacquier & Nicholas G. Polson & Peter Rossi, 1999. "Stochastic Volatility: Univariate and Multivariate Extensions," Computing in Economics and Finance 1999 112, Society for Computational Economics.
  2. Geweke, John, 1989. "Bayesian Inference in Econometric Models Using Monte Carlo Integration," Econometrica, Econometric Society, vol. 57(6), pages 1317-39, November.
  3. BAUWENs, Luc & LUBRANOÂ , Michel, 1996. "Bayesian Inference on GARCH Models using the Gibbs Sampler," CORE Discussion Papers 1996027, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  4. Harvey, Andrew & Ruiz, Esther & Shephard, Neil, 1994. "Multivariate Stochastic Variance Models," Review of Economic Studies, Wiley Blackwell, vol. 61(2), pages 247-64, April.
  5. Osiewalski, Jacek, 1991. "A note on Bayesian inference in a regression model with elliptical errors," Journal of Econometrics, Elsevier, vol. 48(1-2), pages 183-193.
  6. Fernandez, Carmen & Osiewalski, Jacek & Steel, Mark F. J., 1997. "On the use of panel data in stochastic frontier models with improper priors," Journal of Econometrics, Elsevier, vol. 79(1), pages 169-193, July.
  7. Carmen Fernandez & Mark F J Steel, 1998. "Reference priors for the general location-scale model," ESE Discussion Papers 23, Edinburgh School of Economics, University of Edinburgh.
  8. Geweke, J, 1993. "Bayesian Treatment of the Independent Student- t Linear Model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(S), pages S19-40, Suppl. De.
  9. Phillips, P C B, 1991. "To Criticize the Critics: An Objective Bayesian Analysis of Stochastic Trends," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 6(4), pages 333-64, Oct.-Dec..
  10. Shephard, Neil, 1994. "Local scale models : State space alternative to integrated GARCH processes," Journal of Econometrics, Elsevier, vol. 60(1-2), pages 181-202.
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