Some results for the GMANOVA model

Publisher Website
Google Scholar
Abstract
For the generalized MANOVA (GMANOVA) model of potthoff and Roy (1964), Y = 3ξA + E, the densities of the maximum likelihood (m∘1∘) estimators ξ and ξ are obtained. An application of the density of ξ is given to the prediction of a future observation and the density of ξ is shown to be useful for obtaining a test of spharicity. Although the main purpose of the paper is to obtain the densities of ξ and ξ, some results of Glaser and Olkin (G and O) (1970) on testing linear parametric functions if ξ and structure of σ are discussed to stress the importance of the GMANOVA model in Multivariate Analysis. Most of the theory given here is mentioned by G and O (pp. 267-291) in terms of the canoncial transformations of the original variates. However, we wish to acquaint the reader with this theory in terms of the original variates.