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December, 1961 On the Monotonic Character of the Power Functions of Two Multivariate Tests
S. N. Roy, W. F. Mikhail
Ann. Math. Statist. 32(4): 1145-1151 (December, 1961). DOI: 10.1214/aoms/1177704852


The largest characteristic root has been proposed in [2] as a test statistic in (i) the multivariate analysis of variance test, and (ii) testing that two sets of variates are independent. In this paper it is shown that, in each case, the power function is a monotonically increasing function of each non-centrality parameter, separately. This property was stated in [2] without proof. This provides a stronger result than would be obtained by any direct use of Anderson's Theorem [1] which implies that the power function increases when all the roots are simultaneously increased in the same ratio. The proof of the monotonocity property for the multivariate analysis of variance is given in Section 3, and in Section 4 it is shown how the proof is modified for testing independence between two sets of variates.


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S. N. Roy. W. F. Mikhail. "On the Monotonic Character of the Power Functions of Two Multivariate Tests." Ann. Math. Statist. 32 (4) 1145 - 1151, December, 1961.


Published: December, 1961
First available in Project Euclid: 27 April 2007

zbMATH: 0119.35004
MathSciNet: MR130745
Digital Object Identifier: 10.1214/aoms/1177704852

Rights: Copyright © 1961 Institute of Mathematical Statistics

Vol.32 • No. 4 • December, 1961
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