**8. Concluding remarks**

In this chapter, we discuss LRC in multivariate linear model, focusing on the role of projection matrices. Testing problems considered involve the hypotheses on selection of variables or no additional information of a set of variables, in addition to a typical linear hypothesis. It may be noted that various LRCs and their distributions are obtained by algebraic methods.

We have not discussed with LRCs for the hypothesis of selection of variables in canonical correlation analysis, and for dimensionality in multivariate linear model. Some results for these problems can be found in [3, 18].

In multivariate analysis, there are some other test criteria such as Lawley-Hotelling trace criterion and Bartlett-Nanda-Pillai trace criterion. For the testing problems treated in this chapter, it is possible to propose such criteria as in [12].

The LRCs for tests of no additional information of a set of variables will be useful in selec‐ tion of variables. For example, it is possible to propose model selection criteria such as AIC (see [19]).
