Optimal Asymptotic Tests

In this chapter we discuss optimal asymptotic tests for simple and composite hypotheses involving a scalar or vector parameter. The basic model is as given in §2 of Chapter 1 and we assume the LAMN condition is satisfied. This general model is used in §§3 and 4. In later sections more restrictive conditions are required. It turns out that the usual statistics such as the Rao’s score statistic, the Neyman statistic, and the likelihood-ratio (LR) statistic exhibit non-standard asymptotic behaviour in the non-ergodic case, as regards efficiency and limit distributions.