The Annals of Statistics

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

Ingram Olkin and Jack L. Tomsky

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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


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