Admissible and Nonadmissible Test in Unit-Root-like Situations

In this paper I investigate the asymptotic behavior of tests for problems with locally asymptotically quadratic likelihood. I present necessary and sufficient conditions for a test to be admissible. Even without these restrictive parametric assumptions, I can show that certain common procedures - like the ADF-test in case no deterministic trend is present or standard tests for restrictions on cointegrating relationships are asymptotically inadmissible. Hence we show the existence of tests which dominate these classical tests for all parameters