Further Contributions to Multivariate Confidence Bounds

In this paper the implications of certain results obtained in earlier papers (Roy Roy, 1954a, b, 1956) on confidence bounds on parametric functions connected with multi-variate normal populations are fully worked out. This leads to a number of confidence bounds, expected to be useful, but hitherto unnoticed, on the characteristic roots connected with (i) one population dispersion matrix, (ii) two population dispersion matrices, (iii) the regression matrix of a p set on a q set, and (iv) the multivariate linear hypothesis on means, including, in particular, the problem of discriminant analysis. Some examples are given in the last section of the paper to illustrate the use of the techniques presented in the earlier sections.