论文标题
关于Chatterjee等级相关的力量
On the power of Chatterjee rank correlation
论文作者
论文摘要
Chatterjee（2021）引入了一个简单的新等级相关系数，引起了最近的关注。该系数具有异常的吸引力，即它不仅估计了Dette等人首先提出的人口数量。 （2013）且仅当基础随机变量是独立的，但在独立性下也是渐近正常时，这是零。本文将Chatterjee的新相关系数与三个已建立的等级相关性进行了比较，这些等级相关性也有助于一致的独立性测试，即Hoeffding的$ D $，Blum-Kiefer-Rosenblatt的$ R $和Bergsma-Dassma-Dassma-Dassma-Dassios-of-daskios-osios-yanagimoto的$τ^*$。根据最近的进步，我们将它们的计算效率对比，并调查其功率与局部旋转和混合替代方案。我们的主要结果表明，不幸的是，Chatterjee的系数是$ D $，$ r $和$τ^*$的比率。对于Dette等人的相关较早估计器而言，情况更为微妙。 （2013）。这些结果有利于$ D $，$ r $和$τ^*$而不是Chatterjee的新相关系数，以测试独立性。
Chatterjee (2021) introduced a simple new rank correlation coefficient that has attracted much recent attention. The coefficient has the unusual appeal that it not only estimates a population quantity first proposed by Dette et al. (2013) that is zero if and only if the underlying pair of random variables is independent, but also is asymptotically normal under independence. This paper compares Chatterjee's new correlation coefficient to three established rank correlations that also facilitate consistent tests of independence, namely, Hoeffding's $D$, Blum-Kiefer-Rosenblatt's $R$, and Bergsma-Dassios-Yanagimoto's $τ^*$. We contrast their computational efficiency in light of recent advances, and investigate their power against local rotation and mixture alternatives. Our main results show that Chatterjee's coefficient is unfortunately rate sub-optimal compared to $D$, $R$, and $τ^*$. The situation is more subtle for a related earlier estimator of Dette et al. (2013). These results favor $D$, $R$, and $τ^*$ over Chatterjee's new correlation coefficient for the purpose of testing independence.
