On estimation and testing in the generalized multivariate linear model.

This dissertation is concerned with two areas in statistics, namely, estimation of the unknown parameter matrix and testing the general linear hypothesis in two multivariate linear models. The first model is the generalized multivariate model as proposed by Potthoff and Roy, the second is a special case of the first and is referred to as the usual multivariate model. The discussion is divided into six chapters. In Chapter II, mean-squared error estimators for the parameter matrix are found in the generalized multivariate model when the covariance matrix is possibly singular. In Chapter III, mean-squared error estimators are found when the usual multivariate model is restricted by a system of linear constraints. The estimators are given when the covariance matrix is either positive definite or positive semidefinite. In Chapter IV, the estimators from Chapter III are used with a normality assumption to develop the procedures for testing the general linear hypothesis in the less than full rank model. Examples are given for two multivariate analysis of variance models.