ORTHOGONALITY OF HYPOTHESE AND IDENTIFIABILITY CONSTRAINTS IN THE ANALYSIS OF VARIANCE MODEL

We consider a sequence of hypotheses Hi : fi=O, i=1, 2, • , k, in a liner statistical model y=Xft+e=Xlfll+X2J92+ +Xkftk+e. We assume that X is not of full rank —in the analysis of variance model— suitable identifiability constraints B8=O are given in the model. First, we give some results on the orthogonality of hypotheses by introducing the null space representation for the hypotheses. Then, we confine our model to the analysis of variance model and discuss the relationship between orthogonality of hypotheses and identifiability constraints. A method for finding the identifiability constraints which make all the considerable hypotheses orthogonal is proposed.