Some Further Results in Simultaneous Confidence Interval Estimation

This paper is a follow-up of a previous paper 1, the full implications of some of the results there being brought out here in terms that are physically more meaningful. Two cases of simultaneous confidence bounds, I and II, are given, in each case with a confidence coefficient which is to be greater than or equal to a preassigned level. Case I relates to the characteristic roots of and ₁^-1₂, where stands for the dispersion matrix of one p-variate and ₁ and ₂ for the dispersion matrices of two p-variate normal populations. Case II relates to a (p + q) -variate normal population (p q), for which the matrix of regression of the p-set on the q-set is defined in a natural manner. This matrix is denoted by (p q) and simultaneous confidence bounds are given on all bilinear compounds of this matrix (with arbitrary coefficient vectors of unit modulus). Confidence bounds on the characteristic roots of and ₁^-1₂ are given respectively by (3. 1. 3) and (3. 2. 8). Confidence bounds on the bilinear compounds of the regression matrix are given by (4. 7).