Asymptotic Normality of Poly-T Densities with Bayesian Applications.
Technical rept. 1 Sep 85-1 Aug 87,
DEWITT WALLACE RESEARCH LAB NEW YORK
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A poly-t density is a density which is proportional to a product of at least two t-like factors, each of which is of a certain form where d is a positive number, micron underlined is an arbitrary location vector and M underlines is a symmetric semi-positive definite scale matrix. In general, M underlines is a function of d. Such a density arises, for example, in the Bayesian analysis of a linear model with a normal error term, independent normal priors on the linear parameters and inverted-gamma priors on the variance components. A theorem about the asymptotic normality of the density as a subset of the individual ds tend to infinity is proved under very general conditions. A corollary specifically related to the Bayesian linear regression model with two variance components. The Tiao-Zellner expansion for approximating the particular poly-t form involving two proper multivariate t factors is extended to the case of two arbitrary t-like factors.
- Statistics and Probability