## The Annals of Statistics

- Ann. Statist.
- Volume 9, Number 4 (1981), 792-802.

### A New Class of Multivariate Tests Based on the Union-Intersection Principle

Ingram Olkin and Jack L. Tomsky

#### Abstract

Using Roy's union-intersection principle, a unified treatment is developed for the construction of multivariate tests. These include Wilks' determinantal criteria, Hotelling-Lawley trace criterion, and Roy's largest characteristic root criterion. The key lies in the extension of an index set from vectors to matrices plus the use of elementary symmetric functions of characteristic roots to test component hypotheses.

#### Article information

**Source**

Ann. Statist., Volume 9, Number 4 (1981), 792-802.

**Dates**

First available in Project Euclid: 12 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aos/1176345519

**Digital Object Identifier**

doi:10.1214/aos/1176345519

**Mathematical Reviews number (MathSciNet)**

MR619282

**Zentralblatt MATH identifier**

0471.62048

**JSTOR**

links.jstor.org

**Subjects**

Primary: 62H12: Estimation

Secondary: 60E15: Inequalities; stochastic orderings

**Keywords**

Union-intersection principle multivariate tests characteristic roots elementary symmetric functions multivariate linear hypothesis sphericity test testing for the equality of covariance matrices monotonicity of power function

#### Citation

Olkin, Ingram; Tomsky, Jack L. A New Class of Multivariate Tests Based on the Union-Intersection Principle. Ann. Statist. 9 (1981), no. 4, 792--802. doi:10.1214/aos/1176345519. https://projecteuclid.org/euclid.aos/1176345519