Posterior moments of scale parameters in elliptical regression models
AbstractIn the general multivariate elliptical class of data densities we define a scalar precision parameter r through a normalization of the scale matrix V. Using the improper prior on r which preserves the results under Normality for all other parameters and prediction, we consider the posterior moments of r. For the subclass of scale mixtures of Normals we derive the Bayesian counterpart to a sampling theory result concerning uniformly minimum variance unbiased estimation of 7. 2 • If the sampling variance exists, we single out the common variance factor i' as the scalar multiplying V in this sampling variance. Moments of i' are examined for various elliptical subclasses and a sampling theory result regarding its unbiased estimation is mirrored.
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Multivariate elliptical data densities; Bayesian analysis; Unbiased estimation;
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- Fernández, C. & Steel, M.F.J., 1996. "On Bayesian Inference under Sampling from Scale Mixtures of Normals," Discussion Paper 1996-02, Tilburg University, Center for Economic Research.
- Fernández, Carmen & Osiewalski, Jacek & Steel, Mark F. J., 2001.
"Robust Bayesian Inference on Scale Parameters,"
Journal of Multivariate Analysis,
Elsevier, vol. 77(1), pages 54-72, April.
- Fernández, C. & Osiewalski, J. & Steel, M.F.J., 1996. "Robust Bayesian Inference on Scale Parameters," Discussion Paper 1996-65, Tilburg University, Center for Economic Research.
- Carmen Fernandez & Jacek Osiewalski & M. F. J. Steel, 2004. "Robust Bayesian inference on scale parameters," ESE Discussion Papers 25, Edinburgh School of Economics, University of Edinburgh.
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