Remarks on Multivariate Confidence Bounds.
VIRGINIA POLYTECHNIC INST AND STATE UNIV BLACKSBURG DEPT OF STATISTICS
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Confidence bounds are given for all bilinear forms athetab in the parameters of the multivariate linear model using any phi belonging to the class Phi of functions increasing in the eigenvalues of a random matrix. An extension yields simultaneous tests for all hypotheses H AThetaB 0 using any phi epsilon Phi. The optimality of the Roy-Bose bounds for athetab in the class Phi is established. These findings are consequences of a variational lemma which yields bounds on the joint distribution of Friedmans statistics even in small samples. Author
- Statistics and Probability