We follow up on Shi et al's (2020) and Cao's and my (2020) work on the local power of a new test for independence, Chatterjee (2019), and its relation to the local power properties of classical tests. We show quite generally that for testing independence with local alternatives either Chatterjee's rank test has no power, or it may be misleading: The Blum, Kiefer, Rosenblatt, and other omnibus classical rank tests do have some local power in any direction other than those where significant results may be misleading. We also suggest methods of selective inference in independence testing. Chatterjee's statistics like Renyi's (1959) also identified functional dependence. We exhibit statistics which have better power properties than Chatterjee's but also identify functional dependence.
翻译:我们普遍地表明,用地方替代品测试独立与否,查特杰(Chatterjee)(Chatterjee)(202020年)和曹操和我本人(2020年)的工作涉及独立新测试的当地权力(Chatterjee)(2019年)及其与古典测试的当地权力特性的关系。我们相当普遍地表明,查特杰(Chatterjee)的等级测试要么是没有权力的,要么是误导性的:Blum、Kiefer、Rosenblatt(Rosenblatt)和其他古典统括级测试在除重大结果可能误导之外的任何方向上都有一些地方权力。我们还提出了独立测试中选择性推断的方法。查特杰(Chatterje)的统计(Renyi)(1959年)也确认了功能依赖性。我们展示了比查特杰(Chatterjee)更好的权力特性,但也有功能依赖性的统计数据。