论文标题
独立性和功能依赖性的度量
Measures of independence and functional dependence
论文作者
论文摘要
我们跟进Shi等人（2020年）和CAO和我的（2020年）的作品，该作品是针对独立的新测试的当地力量，Chatterjee（2019），以及它与经典测试的本地权力属性的关系。我们一般表明，对于Chatterjee的排名测试测试独立性，要么没有权力，要么可能具有误导性：Blum，Kiefer，Rosenblatt和其他综合经典等级测试确实在任何方向上都具有一定的局部力量，这些方向除了重大结果可能会误导性。我们还建议在独立性测试中选择性推断的方法。 Chatterjee的统计数据（1959年）也确定了功能依赖性。我们展示的统计数据比Chatterjee具有更好的功率特性，但也确定了功能依赖性。
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.
