Nonnull and Optimality Robustness of Some Tests

Abstract

This paper first characterizes the invariant structure of a model for which nonnull robustness holds. Applications of this result yield the nonnull robustness and optimality robustness of some tests for covariance structure including a test for sphericity. Second, we show the optimality robustness of the LBI tests in the GMANOVA(MANOVA) problem, and the problem of testing independence. In the GMANOVA problem, a robustness property of an essentially complete class of invariant tests is also shown.