Generalized Measures of Correlation for Asymmetry, Nonlinearity, and Beyond
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刻画非对称性与非线性的广义相关度量
- 研究问题
- 当两个变量相互解释方差的能力不对称且关系可能非线性时，如何构造比传统相关系数更有针对性的度量与检验？
- 方法与思路
- 作者提出成对的广义相关度量，研究其理论性质及核估计量的联合渐近分布，并据此检验解释方差能力是否对称。
- 材料陈述的贡献
- 摘要称部分情形下两项度量相等且等于 Pearson 相关系数的平方，并给出对称性检验、模拟和经济金融指标应用。
- 阅读关注点
- 核对解释方差的方向性定义、退化为平方相关系数的条件、核估计的调参和检验条件，并区分预测关联与因果解释。
- 阅读边界
- 材料为 OpenAlex 索引摘要，稿件版本未注明；具体指标、模型选择规则和改善幅度未说明，相关度量不能直接支持因果判断。
原文摘要
Applicability of Pearson's correlation as a measure of explained variance is by now well understood. One of its limitations is that it does not account for asymmetry in explained variance. Aiming to develop broad applicable correlation measures, we study a pair of generalized measures of correlation (GMC) that deals with asymmetries in explained variances, and linear or nonlinear relations between random variables. We present examples under which the paired measures are identical, and they become a symmetric correlation measure that is the same as the squared Pearson's correlation coefficient. As a result, Pearson's correlation is a special case of GMC. Theoretical properties of GMC show that GMC can be applicable in numerous applications and can lead to more meaningful conclusions and improved decision making. In statistical inference, the joint asymptotics of the kernel-based estimators for GMC are derived and are used to test whether or not two random variables are symmetric in explaining variances. The testing results give important guidance in practical model selection problems. The efficiency of the test statistics is illustrated in simulation examples. In real-data analysis, we present an important application of GMC in explained variances and market movements among three important economic and financial monetary indicators. This article has online supplementary materials.