Fixed size confidence regions for the difference of the means of two multinormal populations

The present paper deals with the problem of constructing a fixed size ellipsoidal confidence region for the difference of the mean vectors of two independent multinormal populations.We have assumed that the covariance matrices of the first and second populations are respectively given by σ2 1H and σ2 2 H, where σ2 1 and σ2 2 are both unknown. Here H is assumed to be a known positive definite matrix. The two cases, namely,(i)σ1 = σ2 and equal sample sizes and (ii)σ1 ≠ σ2 and unequal sample sizes have been dealt with separately. We propose both two stage and sequential procedures for each problem and study various exact and asymptotic Properties of these procedures through several theorems. Moderate samplesize performances of our proposed sampling rules have also been studied and these are found to be very satisfactory.