Publication: Posterior moments of scale parameters in elliptical regression models
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1992-02
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Abstract
In 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