Robustness of Multivariate Tests

The Annals of Statistics · 1981 · Volume 9 · Issue 6

Abstract

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.

Keywords

62C07, 62H15, elliptic symmetry, Left $\mathscr{O} (n)$-invariant distribution, MANOVA and GMANOVA problem, robustness, spherical symmetry, Stiefel manifold, tests of independence

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