## 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

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

#### 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