A New Coefficient of Correlation
A New Coefficient of Correlation
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DOI：
10.1080/01621459.2020.1758115
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发表时间：
2020-05-28
影响因子：
3.7
通讯作者：
Chatterjee, Sourav
中科院分区：
文献类型：
--
作者：
Chatterjee, Sourav
有没有可能定义一个相关系数，它（a）像皮尔逊相关系数或斯皮尔曼相关系数一样简单，但（B）始终估计变量之间依赖程度的一些简单和可解释的度量，当且仅当变量独立时为0，当且仅当一个变量是另一个变量的可测量函数时为1，和（c）有一个简单的渐近理论的假设下的独立性，像经典的系数？本文通过提出这样一个系数，肯定地回答了这个问题。不需要对变量的分布做任何假设。文献中有几个系数收敛到0当且仅当变量是独立的，但没有一个满足上述任何其他属性。
Is it possible to define a coefficient of correlation which is (a) as simple as the classical coefficients like Pearson's correlation or Spearman's correlation, and yet (b) consistently estimates some simple and interpretable measure of the degree of dependence between the variables, which is 0 if and only if the variables are independent and 1 if and only if one is a measurable function of the other, and (c) has a simple asymptotic theory under the hypothesis of independence, like the classical coefficients? This article answers this question in the affirmative, by producing such a coefficient. No assumptions are needed on the distributions of the variables. There are several coefficients in the literature that converge to 0 if and only if the variables are independent, but none that satisfy any of the other properties mentioned above.for this article are available online.