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Testing Problems in GMANOVA
Testing on Some Covariance Structure
Identifiability of Hypotheses
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acting action addition admissible apply approach assumed assumption asymptotic called canonical form Chapter coefficient compact complete condition consider covariance matrix covariance structure critical defined Definition denotes density depend derived equal equation equivalent estimator evaluated Example exists expressed extended GMANOVA problem fact follows Further G-invariant given GLSE GMANOVA model GMANOVA problem growth hand Hence holds hypothesis implies independent integration invariant test Kariya known LBI test leaving Lemma likelihood ratio linear locally maximal invariant means measure minimax monotonicity multivariate normal noted null distribution observed obtain OLSE parameter power function probability problem of testing proof prove rank reduced regarded respect restriction result sample satisfying Section shown similar space subgroup sufficient condition term test based testing problem Theorem transformation treated UMPI usual variant versus yields