| Abstract: | For hypothesis testing in curved bivariate normal families we compare various size a tests by means of their Hodges-Lehmann efficacies at fixed alternatives, in particular when these tests have equal optimal asymptotic power in the local Pitman sense. The locally most powerful tests and the likelihood ratio tests for the curve are both Pitman optimal, but the latter turn out to have higher Hodges-Lehmann efficacy. All the tests considered here, including the locally most powerful tests, are likelihood ratio tests against suitable (possibly enlarged) sets of alternatives, the curve itself being an important special case of such a subset. In passing we illustrate a general result in Brown (1971) concerning Hodges-Lehmann optimality obtained by enlarging the model. |
