One important aspect of statistical inference is testing the hypothesis of interest. In the context of multivariate linear models, the hypotheses may be functions of
matrix B only,
matrix Σ only, or
both B and Σ.
A hypothesis on B may be of interest in a variety of situations. It may be needed in the context of data reduction, to test the redundancy of certain variables, or in connection with model reduction schemes as in the process of selecting variables. Of course a number of hypotheses are important in their own right, e.g., when a ...