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Spherically Symmetric Distributions
Invariance Approach to Testing
General Approach to the Robustness of Tests
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3.5 of Chapter ancillary statistics assumed Assumption 3.3 bijective canonical form class of level class of tests completes the proof consider convex Corollary covariance structure critical region defined denotes density derived elliptically symmetric distributions evaluated f-distribution f-test given GL(p GMANOVA model GMANOVA problem GU(p Hence homeomorphism implies independent of q invariant measure invariant probability measure invariant test latent roots LBI test Lebesgue measure left-invariant measure level a tests locally best invariant locally compact MANOVA maximal invariant multivariate multivariate normal distribution n x p Neyman-Pearson lemma nonnull robustness normal distribution null distribution null hypothesis null robustness optimality robustness orthogonal orthogonal matrices parameter power function probability measure probability ratio problem of testing respect satisfies Section 3.2 serial correlation sigma-compact space spherical sufficient statistic test based test statistic test with critical testing H testing problems Theorem 1.1 topological UMPI for testing versus Wijsman