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March, 1964 Monotonicity of the Power Functions of Some Tests of the Multivariate Linear Hypothesis
S. Das Gupta, T. W. Anderson, G. S. Mudholkar
Ann. Math. Statist. 35(1): 200-205 (March, 1964). DOI: 10.1214/aoms/1177703742


The test procedures, invariant under certain groups of transformations [4], for testing a set of multivariate linear hypotheses in the linear normal model depend on the characteristic roots of a random matrix. The power function of such a test depends on the characteristic roots of a corresponding population matrix as parameters; these roots may be regarded as measures of deviation from the hypothesis tested. In this paper sufficient conditions on the procedure for the power function to be a monotonically increasing function of each of the parameters are obtained. The likelihood-ratio test [1], Lawley-Hotelling trace test [1], and Roy's maximum root test [6] satisfy these conditions. The monotonicity of the power function of Roy's test has been shown by Roy and Mikhail [5] using a geometrical method.


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S. Das Gupta. T. W. Anderson. G. S. Mudholkar. "Monotonicity of the Power Functions of Some Tests of the Multivariate Linear Hypothesis." Ann. Math. Statist. 35 (1) 200 - 205, March, 1964.


Published: March, 1964
First available in Project Euclid: 27 April 2007

zbMATH: 0211.50404
MathSciNet: MR158474
Digital Object Identifier: 10.1214/aoms/1177703742

Rights: Copyright © 1964 Institute of Mathematical Statistics

Vol.35 • No. 1 • March, 1964
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