The Annals of Mathematical Statistics

Monotonicity of the Power Functions of Some Tests of the Multivariate Linear Hypothesis

S. Das Gupta, T. W. Anderson, and G. S. Mudholkar

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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.

Article information

Source
Ann. Math. Statist., Volume 35, Number 1 (1964), 200-205.

Dates
First available in Project Euclid: 27 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aoms/1177703742

Digital Object Identifier
doi:10.1214/aoms/1177703742

Mathematical Reviews number (MathSciNet)
MR158474

Zentralblatt MATH identifier
0211.50404

JSTOR
links.jstor.org

Citation

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


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