Some Power Comparisons of Joint and Paired Tests for Nonnested Models under Local Hypotheses

This paper compares the asymptotic local power properties of some tests of a null model against a single nonnested alternative and against multiple nonnested alternatives, denoted hereafter as paired and joint tests, respectively. It is demonstrated that the ranking of tests on the basis of asymptotic local powers depends on the choice of local hypothesis. When a local null hypothesis is employed, it is not possible to rank the Wald and Cox-type paired or joint tests. However, when the local hypothesis is specified with reference to one of the alternative models under consideration, a ranking of different test procedures becomes possible. Under a local alternative hypothesis, it is shown that the paired Wald test will never have greater asymptotic local power than a paired Cox-type test.