Global power functions of goodness of fit tests

• 成果类型: Article
• 署名作者: Janssen, A
• 署名单位: Heinrich Heine University Dusseldorf
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1016120371
• 发表日期: 2000
• 页码: 239-253
• 关键词: kolmogorov-smirnov test; of-fit; asymptotic power; ALTERNATIVES

摘要

It is shown that the global power function of any nonparametric test is flat on balls of alternatives except for alternatives coming from a finite dimensional subspace. The present benchmark is here the upper one-sided (or two-sided) envelope power function. Every choice of a test fixes a priori a finite dimensional region with high power. It turns out that also the level points are far away from the corresponding Neyman-Pearson test level points except for a finite number of orthogonal directions of alternatives. For certain submodels the result is independent of the underlying sample size. In the last section the statistical consequences and special goodness of fit tests are discussed.