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On Bayesian Inference under Sampling from Scale Mixtures of Normals

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Author Info

  • Fernández, C.
  • Steel, M.F.J.

    (Tilburg University, Center for Economic Research)

Abstract

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 precision 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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Bibliographic Info

Paper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 1996-02.

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Date of creation: 1996
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Handle: RePEc:dgr:kubcen:199602

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Web page: http://center.uvt.nl

Related research

Keywords: Bayesian Statistics; Linear Regression;

References

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  1. Harvey, Andrew & Ruiz, Esther & Shephard, Neil, 1994. "Multivariate Stochastic Variance Models," Review of Economic Studies, Wiley Blackwell, vol. 61(2), pages 247-64, April.
  2. Geweke, John, 1989. "Bayesian Inference in Econometric Models Using Monte Carlo Integration," Econometrica, Econometric Society, vol. 57(6), pages 1317-39, November.
  3. 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.
  4. Fernández, C. & Osiewalski, J. & Steel, M.F.J., 1995. "Inference robustness in multivariate models with a scale parameter," Discussion Paper 1995-25, Tilburg University, Center for Economic Research.
  5. Osiewalski, J. & Steel, M., 1990. "Robust Bayesian Inference In Elliptical Regression Models," Papers 9032, Tilburg - Center for Economic Research.
  6. 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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Citations

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Cited by:
  1. Carmen Fernandez & M. F. J. Steel, 2004. "Reference priors for the general location-scale model," ESE Discussion Papers 23, Edinburgh School of Economics, University of Edinburgh.
  2. Fernández, C. & Steel, M.F.J., 1996. "On Bayesian Modelling of Fat Tails and Skewness," Discussion Paper 1996-58, Tilburg University, Center for Economic Research.
  3. 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.
  4. Carmen Fernandez & M. F. J. Steel, 2004. "On the dangers of modelling through continuous distributions: A Bayesian perspective," ESE Discussion Papers 22, Edinburgh School of Economics, University of Edinburgh.
  5. Tsionas, Efthymios G., 1998. "Monte Carlo inference in econometric models with symmetric stable disturbances," Journal of Econometrics, Elsevier, vol. 88(2), pages 365-401, November.

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