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December, 1963 On a Paradox Concerning Inference About a Convariance Matrix
A. P. Dempster
Ann. Math. Statist. 34(4): 1414-1418 (December, 1963). DOI: 10.1214/aoms/1177703873


Suppose a $p \times p$ dispersion matrix $\mathbf{T}$ is considered to have the Wishart distribution $W (\Sigma, n)$, c. f. Anderson (1958) p. 158, where $\Sigma$ is an arbitrary full rank covariance matrix and $n \geqq p$. Suppose $\mathbf{T}$ is observable but $\Sigma$ is unknown, and suppose a posterior distribution is to be assigned to $\Sigma$ given $\mathbf{T}$, where the term posterior is meant in a wide sense to allow the use of a Bayesian or fiducial or any other form of reasoning in arriving at the posterior distribution. A lemma is proved in Section 3 giving a property of all such posterior distributions which possess a natural linear invariance property. The paradoxical nature of this property is discussed in Section 4.


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A. P. Dempster. "On a Paradox Concerning Inference About a Convariance Matrix." Ann. Math. Statist. 34 (4) 1414 - 1418, December, 1963.


Published: December, 1963
First available in Project Euclid: 27 April 2007

zbMATH: 0124.35201
MathSciNet: MR156399
Digital Object Identifier: 10.1214/aoms/1177703873

Rights: Copyright © 1963 Institute of Mathematical Statistics

Vol.34 • No. 4 • December, 1963
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