Further Results on Tests of Separate Families of Hypotheses

SUMMARY It is required to test a composite null hypothesis. High power is desired against a composite alternative hypothesis that is not in the same parametric family as the null hypothesis. In an earlier paper a modification of the Neyman-Pearson maximum-likelihood ratio test was suggested for this problem. The present paper gives some general comments on the formulation of the problem, a general large-sample form for the test, and, finally, a number of examples.