A new approximate point optimal test of a composite null hypothesis

In this paper, we use the generalized Neyman–Pearson lemma to introduce a new approximate point optimal test that can be used for testing a composite null hypothesis against a composite alternative. The new test involves finding multiple critical values. Two methods for obtaining these critical values are outlined. We report simulations of the application of this test to two composite non-nested testing problems, namely testing for first-order moving average (MA(1)) errors against first-order autoregressive (AR(1)) errors in the linear regression model and testing for AR(1) errors against integrated MA(1) (IMA(1,1)) errors in the linear model. We compare the performance of the new test with Silvapulle and Kingʹs (1991) approximate point optimal test and some asymptotic tests and find that the new test has a clear advantage over the other tests, particularly for the second testing problem.