Summary Chatterjee (2021) introduced a simple new rank correlation coefficient that has attracted much attention recently. 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 with 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 $\tau^*$. We compare the computational efficiency of these rank correlation coefficients 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-suboptimal compared to $D$, $R$ and $\tau^*$. The situation is more subtle for a related earlier estimator of Dette et al. (2013). These results favour $D$, $R$ and $\tau^*$ over Chatterjee’s new correlation coefficient for the purpose of testing independence.

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关于 Chatterjee 等级相关性的力量

总结 Chatterjee (2021) 引入了一个简单的新秩相关系数，最近备受关注。该系数具有不同寻常的吸引力，它不仅估计了 Dette 等人首先提出的人口数量。（2013）当且仅当基础随机变量对是独立的时为零，但在独立下也是渐近正态的。本文将 Chatterjee 的新相关系数与三个已建立的秩相关系数进行了比较，这些相关系数也有助于一致的独立性检验，即 Hoeffding 的 $D$、Blum-Kiefer-Rosenblatt 的 $R$ 和 Bergsma-Dassios-Yanagimoto 的 $\tau^*$。我们根据最近的进展比较了这些等级相关系数的计算效率，并研究了它们对抗局部旋转和混合替代方案的能力。我们的主要结果表明，不幸的是，与 $D$、$R$ 和 $\tau^*$ 相比，Chatterjee 的系数是速率次优的。对于 Dette 等人的相关早期估计者来说，情况更为微妙。（2013）。为了测试独立性，这些结果有利于 $D$、$R$ 和 $\tau^*$ 而不是 Chatterjee 的新相关系数。