On the power of Chatterjee rank correlation
On the power of Chatterjee rank correlation
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发表时间：
2020-08
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通讯作者：
Hongjian Shi;M. Drton;Fang Han
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作者：
Hongjian Shi;M. Drton;Fang Han
Chatterjee（2021）引入了一个简单的新秩相关系数，最近引起了广泛关注。该系数具有不寻常的吸引力，它不仅估计了Dette等人（2013）首次提出的为零的总体数量，当且仅当潜在的随机变量对是独立的，而且在独立下是渐近正态的。本文比较查特吉的新的相关系数，也有利于一致的独立性测试，即Hoeffding的$D$，Blum-Kiefer-Rosenblatt的$R$，和Bergsma-Dassios-Yanagimoto的$\tau^*$三个既定的等级相关。我们对比他们的计算效率，根据最近的进展，并调查他们的权力对本地旋转和混合物的替代品。我们的主要结果表明，不幸的是，查特吉的系数是次优率相比，$D$，$R$，和$\tau^*$。对于Dette等人（2013）的相关早期估计量，情况更为微妙。这些结果有利于$D$，$R$和$\tau^*$在查特吉的新的相关系数的目的，测试的独立性。
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 $\tau^*$. 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 $\tau^*$. The situation is more subtle for a related earlier estimator of Dette et al. (2013). These results favor $D$, $R$, and $\tau^*$ over Chatterjee's new correlation coefficient for the purpose of testing independence.