Large-Sample Restricted Parametric Tests

SUMMARY Restricted tests are designed to examine a hypothesis not against the natural complete alternative but against some subhypothesis of that alternative. The theory of such tests provides a unification of many aspects of large-sample tests—the analysis of nested hypotheses, the possibility of using tests of increased power and of easing certain computational procedures, the notions of separable hypotheses and of partitioning a test statistic. While many standard results can thus be brought within the framework of this theory the emphasis throughout the paper is on providing the consulting statistician with manageable tools for non-standard situations.