A New Class of Multivariate Tests Based on the Union-intersection Principle |
Common terms and phrases
acceptance region analytic function Anderson Applying Theorem Bahadur efficiency belongs to D(1,1 charac COMPARISON OF TESTS consider Corollary covariance matrix D₂ decreasing order according defined denoted diagonal elements diagonal matrix elementary symmetric functions H is true Hotelling-Lawley hypothesis H intersection k₁ k₁-k k₂ Lemma likelihood ratio component likelihood ratio test limiting distribution linear model max tr maximizes monotonicity property multivariate tests normal distribution null component hypotheses null hypothesis obtain ordered characteristic roots orthogonal matrix partition Pi+l population characteristic root power function Proof ratio component test reject H rejection region respectively roots of ASA S₁ S₂ sample sets of variates simultaneous confidence bounds step-down procedure Suppose symmetric matrix teristic roots test based test statistic Theorem 6.1(iii Theorem 6.2 tr ASA union-intersection principle union-intersection test vector Wishart distribution акр