Abstract
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.
Citation
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. https://doi.org/10.1214/aoms/1177703742
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