Upper Percentage Points of the Intermediate Roots of the Manova Matrix
Abstract
Let S(1) and S(2) be independently distributed as p x p central Wishart matrices with n(1) and n(2) (p < n(1), n(2)) degrees of freedom and let E(S1/n1) = E(S2/n2) = Sigma. Further, let theta(1) < theta(2) < ... < theta(p) be the characteristic roots of S(1) (S(1) + S(2)) -1. Let r = (n(1) - p - 1)/2 and n = (n(2) - p - 1)/2. In the paper, the authors give tables for the exact values of the upper 5% and 1% points of the distribution of theta(2), i = 2, 3, ..., p - 1 for p = 4,5,6,7 and of the distribution of theta(2) and theta(7) for p = 8 when r = 0 (1) 5, 7, 10, 15 and n = 5 (1) 10 (2) 20 (5) 50. These tables were constructed by using the exact expression for the c.d.f. of theta(s) (2 is equal to or less than s is equal to or less than p - 1) given by Krishnaiah and Waikar (J. Multivariate Analysis, 1 (1971)).
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 1972
- Accession Number
- AD0742985
Entities
People
- F. J. Schuurmann
- Paruchuri R. Krishnaiah
- V. B. Waikar
Organizations
- Air Force Research Laboratory