Simultaneous pseudo confidence regions for ratios of the discriminant coefficients

We consider simultaneous confidence regions for some hypotheses on ratios of the discriminant coefficients of the linear discriminant function when the population means and common covariance matrix are unknown. This problem, involving hypotheses on ratios, yields the so-called ‘pseudo’ confidence regions valid conditionally in subsets of the parameter space. We obtain the explicit formulae of the regions and give further discussion on the validity of these regions. Illustrations of the pseudo confidence regions are given.