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On Bayesian inference under sampling from scale mixtures of normals

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Author Info
Fernandez, C.
Steel, M. (Tilburg University, Center for Economic Research)

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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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Paper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 2.

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Date of creation: 1996
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Handle: RePEc:dgr:kubcen:19962

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Keywords: Linear Regression

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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Osiewalski, Jacek & Steel, Mark F. J., 1993. "Robust bayesian inference in elliptical regression models," Journal of Econometrics, Elsevier, vol. 57(1-3), pages 345-363. [Downloadable!] (restricted)
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  2. Geweke, John, 1989. "Bayesian Inference in Econometric Models Using Monte Carlo Integration," Econometrica, Econometric Society, vol. 57(6), pages 1317-39, November. [Downloadable!] (restricted)
  3. Fernandez, C. & Osiewalski, J. & Steel, F.J.M., 1995. "Inference Robustness in Multivariate Models with a Scale Parameter," Papers 9530, Catholique de Louvain - Center for Operations Research and Economics.
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  4. Fernandez, C. & Osiewalski, J. & Steel, M.F.J., 1993. "The Continuous Multivariate Location-Scale Model Revisited: A Tale of Robustness," Papers 9380, Tilburg - Center for Economic Research.
  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. [Downloadable!] (restricted)
  6. 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. [Downloadable!] (restricted)
  7. Fernandez, C. & Steel, M.F.J., 1995. "reference Priors in Non-Normal Location Problems," Papers 9591, Tilburg - Center for Economic Research.
  8. Shephard, Neil, 1994. "Local scale models : State space alternative to integrated GARCH processes," Journal of Econometrics, Elsevier, vol. 60(1-2), pages 181-202. [Downloadable!] (restricted)
  9. Harvey, Andrew & Ruiz, Esther & Shephard, Neil, 1994. "Multivariate Stochastic Variance Models," Review of Economic Studies, Blackwell Publishing, vol. 61(2), pages 247-64, April. [Downloadable!] (restricted)
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  1. Fernandez, C. & Steel, M.F.J., 1997. "On the dangers of modelling through continuous distributions : a Bayesian perspective," Discussion Paper 5, Tilburg University, Center for Economic Research. [Downloadable!]
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  2. Fernandez, C. & Steel, M.F.J., 1997. "Reference priors for the general location-scale model," Discussion Paper 105, Tilburg University, Center for Economic Research. [Downloadable!]
    Other versions:
  3. Fernandez, C. & Steel, M.F.J., 1996. "On Bayesian modelling of fat tails and skewness," Discussion Paper 58, Tilburg University, Center for Economic Research. [Downloadable!]
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