A New Method for Testing Separate Families of Hypotheses
针对Cox和Williams检验分离假设族时存在的根本缺陷，提出一种基于参数自助法的新方法，通过重复应用并逐步缩小置信区域来保证渐近水平，并给出理论性质和有限样本表现。
Abstract Theoretical and empirical evidence are reported showing that the tests given in Cox (1961) and Williams (1970a, b) for the problem of testing separate families of hypotheses suffer from fundamental difficulties. Neither test is guaranteed to be asymptotically level a, even for very smooth problems. A new method proposed here as an alternative works adaptively by repeated application of the parametric bootstrap idea over slowly shrinking confidence regions. Theoretical properties of the method are derived, and its finite-sample behavior is studied in a number of examples.