Yasunori Fujikoshi

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/62277

#### **Abstract**

The aim of this chapter is to review likelihood ratio test procedures in multivariate linear models, focusing on projection matrices. It is noted that the projection matrices to the spaces spanned by mean vectors in hypothesis and alternatives play an important role. Some basic properties are given for projection matrices. The models treated include multivariate regression model, discriminant analysis model, and growth curve model. The hypotheses treated involve a generalized linear hypothesis and no additional information hypothesis, in addition to a usual liner hypothesis. The test statistics are expressed in terms of both projection matrices and sums of squares and products matrices.

**Keywords:** algebraic approach, additional information hypothesis, generalized linear hypothesis, growth curve model, multivariate linear model, lambda distribution, like‐ lihood ratio criterion (LRC), projection matrix
