ABSTRACT
This chapter considers some basic results that are encountered in introductory courses on multivariate analysis and linear models using a matrix-based formulation. The purpose is to provide some details of the techniques used to establish these results, giving cross-references to those sections where the techniques are established. Keeping this aim in mind means that only very brief descriptions are given of important topics such as principal components analysis, discriminant analysis and so on and little discussion of their purpose and interpretation is included since the information is readily available in standard specialist texts. For the construction of likelihood ratio tests people need the actual form of the maximized likelihood under null and alternative hypotheses. The chapter illustrates some of the techniques and results established earlier by showing how these can be used to construct likelihood ratio test statistics and to evaluate them numerically in cases where data have been obtained.
