TESTING NONNESTED LINEAR HYPOTHESES I : REDUCTION BY INVARIANCE CONSIDERATIONS

This paper is concerned with the problem of testing nonnested linear hypotheses. The problem is expressed in terms of the relevant linear (vector) subspaces. The "degree of nonnestedness" of the hypotheses is examined. After a suitable linear transformation, the vector of observations is reduced by invariance considerations to a 2—dimensional statistic. It is shown that the power function of invariant tests depends on the regressor matrices through certain characteristic numbers which measure "the degree of nonnestedness" of the linear hypotheses