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December, 1956 Some Results Useful in Multivariate Analysis
K. C. S. Pillai
Ann. Math. Statist. 27(4): 1106-1114 (December, 1956). DOI: 10.1214/aoms/1177728076


In this paper a few results (of a purely mathematical nature) are obtained, which are useful for studying certain distribution problems in multivariate analysis--e.g., those relating to the characteristic roots of a determinantal equation ([1], [2], [5]). In particular, the results are shown to be readily applicable to the moment problems of the sum of the roots and the distributions of the extreme roots. Most of the results given are in the form of certain recursion formulae for reducing special types of $k$-th order Vandermonde determinants in terms of those of orders $(k - 1)$ and $(k - 2).$ The applications of these results are given by S. N. Roy [6] and the present author [3].


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K. C. S. Pillai. "Some Results Useful in Multivariate Analysis." Ann. Math. Statist. 27 (4) 1106 - 1114, December, 1956.


Published: December, 1956
First available in Project Euclid: 28 April 2007

zbMATH: 0073.13701
MathSciNet: MR81852
Digital Object Identifier: 10.1214/aoms/1177728076

Rights: Copyright © 1956 Institute of Mathematical Statistics

Vol.27 • No. 4 • December, 1956
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