On Confidence Bounds Associated with Multivariate Analysis of Variance and Non-Independence Between Two Sets of Variates

Abstract

A theory of simultaneous confidence bounds on certain parametric functions, and their `partials,' associated with some problems in multivariate normal statistical analysis has been developed by S. N. Roy and his associates in a series of publications over the past decade (e.g., [6], [7], [8], also see the references in [8]). In this paper we have obtained simultaneous confidence bounds on the members of a class of parametric functions, together with their `partials,' associated with the two problems mentioned in the title. Our results, not only contain Roy's results as particular cases but, also throw a new light on the parametric functions used by Roy. Furthermore, confidence bounds, which can be considered as being associated with Hotelling's trace criterian for the MANOVA problem can be obtained as an example from our results.