Remarks on Multivariate Confidence Bounds.
Abstract
Confidence bounds are given for all bilinear forms a'(theta)b 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: A'(Theta)B = 0 using any phi epsilon Phi. The optimality of the Roy-Bose bounds for a'(theta)b in the class Phi is established. These findings are consequences of a variational lemma which yields bounds on the joint distribution of Friedman's statistics even in small samples. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jul 15, 1973
- Accession Number
- AD0763463
Entities
People
- Donald R. Jensen
Organizations
- Virginia Tech