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November, 1981 Robustness of Multivariate Tests
Takeaki Kariya
Ann. Statist. 9(6): 1267-1275 (November, 1981). DOI: 10.1214/aos/1176345643


This paper gives necessary and sufficient conditions for the null distribution of a test statistic to remain the same in the class of left $\mathscr{O}(n)$-invariant distributions and in the class of elliptically symmetric distributions. Secondly, it is shown that in certain special cases, the usual MANOVA tests are still uniformly most powerful invariant in a class of left $\mathscr{O}(n)$-invariant distributions including elliptically symmetric distributions.


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Takeaki Kariya. "Robustness of Multivariate Tests." Ann. Statist. 9 (6) 1267 - 1275, November, 1981.


Published: November, 1981
First available in Project Euclid: 12 April 2007

zbMATH: 0474.62048
MathSciNet: MR630109
Digital Object Identifier: 10.1214/aos/1176345643

Primary: 62H15
Secondary: 62C07

Keywords: elliptic symmetry , Left $\mathscr{O} (n)$-invariant distribution , MANOVA and GMANOVA problem , robustness , spherical symmetry , Stiefel manifold , tests of independence

Rights: Copyright © 1981 Institute of Mathematical Statistics

Vol.9 • No. 6 • November, 1981
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