The Annals of Mathematical Statistics
- Ann. Math. Statist.
- Volume 35, Number 1 (1964), 200-205.
Monotonicity of the Power Functions of Some Tests of the Multivariate Linear Hypothesis
The test procedures, invariant under certain groups of transformations , 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 , Lawley-Hotelling trace test , and Roy's maximum root test  satisfy these conditions. The monotonicity of the power function of Roy's test has been shown by Roy and Mikhail  using a geometrical method.
Ann. Math. Statist., Volume 35, Number 1 (1964), 200-205.
First available in Project Euclid: 27 April 2007
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Gupta, S. Das; Anderson, T. W.; Mudholkar, G. S. Monotonicity of the Power Functions of Some Tests of the Multivariate Linear Hypothesis. Ann. Math. Statist. 35 (1964), no. 1, 200--205. doi:10.1214/aoms/1177703742. https://projecteuclid.org/euclid.aoms/1177703742