On the asymptotic power and relative efficiency of the frequency X2 test

The asymptotic (Pitman) power of the X² test is investigated for particular classes of alternatives. A simple rule is introduced to identify ‘orthogonal alternatives’, for which the noncentrality parameter can be computed in a very simple way. In the sequel, restricted alternatives are considered and the ARE of the unrestricted test w.r.t. the restricted one is shown to depend only on the numbers of degrees of freedom. The concluding section discusses ‘undetectable alternatives’, i.e. alternatives for which the noncentrality vanishes.