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April, 1969 Biorthogonal and Dual Configurations and the Reciprocal Normal Distribution
Robert H. Berk
Ann. Math. Statist. 40(2): 393-398 (April, 1969). DOI: 10.1214/aoms/1177697703


In this note we discuss the notions of biorthogonal and dual configurations and their relevance in certain statistical applications. The first application is to the distribution of a random matrix related to a multi-variate-normal sample matrix. As with the latter, the distribution is preserved by (certain) linear transformations. One consequence of this is the familiar result that if $\mathbf{Q}$ is a non-singular Wishart matrix, then for any non-zero vector $\alpha, 1/\alpha'\mathbf{Q}^{-1}\alpha$ is a multiple of a chi-square variable. Application is also made to the Gauss-Markov theorem and to certain estimates of mixing proportions due to Robbins.


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Robert H. Berk. "Biorthogonal and Dual Configurations and the Reciprocal Normal Distribution." Ann. Math. Statist. 40 (2) 393 - 398, April, 1969.


Published: April, 1969
First available in Project Euclid: 27 April 2007

zbMATH: 0174.22307
MathSciNet: MR238433
Digital Object Identifier: 10.1214/aoms/1177697703

Rights: Copyright © 1969 Institute of Mathematical Statistics


Vol.40 • No. 2 • April, 1969
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