Asymptotically Similar Tests of a Composite Hypothesis Versus a Nonstationary Alternative

A general method for the formulation of asymptotically similar tests, based on access to $\sqrt{n}$-consistent estimates of an unknown parameter, is described for the problem of testing a composite hypothesis against a nonstationary alternative. The asymptotically most powerful test is chosen in the class of differentially asymptotically similar tests. Cases in which the similarity constraints do not sacrifice efficiency are treated separately.