Quotient correlation: A sample based alternative to Pearson’s correlation
商相关：基于样本的 Pearson 相关替代指标AI 解读 ↓
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AI 根据所提供的论文材料归类：摘要讨论一般依赖与互联网流量，尾部分析本身不足以归入金融尾部风险方向。
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商相关：基于样本的 Pearson 相关替代指标
- 研究问题
- 当非线性依赖或尾部行为使常规相关系数难以有效刻画关系时，如何构造相关指标及相应的依赖检验？
- 方法与思路
- 作者定义商相关、尾部商相关和基于秩的商相关，并构造极限分布为 Gamma 分布的依赖及尾部独立性检验统计量。
- 材料陈述的贡献
- 摘要称这些指标可刻画非线性与尾部依赖，并在模拟和互联网流量分析中展示优势，部分场景下检验功效较高。
- 阅读关注点
- 核对指标的定义域、边际标准化与尾部调整方式，以及 Gamma 极限的条件和相对 Fisher 变换检验的比较场景。
- 阅读边界
- 依据版本未注明的 OpenAlex 索引摘要；摘要未说明尾部阈值、完整分布条件或功效数值，不能认定其普遍优于其他相关指标。
原文摘要
The quotient correlation is defined here as an alternative to Pearson’s correlation that is more intuitive and flexible in cases where the tail behavior of data is important. It measures nonlinear dependence where the regular correlation coefficient is generally not applicable. One of its most useful features is a test statistic that has high power when testing nonlinear dependence in cases where the Fisher’s Z-transformation test may fail to reach a right conclusion. Unlike most asymptotic test statistics, which are either normal or χ2, this test statistic has a limiting gamma distribution (henceforth, the gamma test statistic). More than the common usages of correlation, the quotient correlation can easily and intuitively be adjusted to values at tails. This adjustment generates two new concepts—the tail quotient correlation and the tail independence test statistics, which are also gamma statistics. Due to the fact that there is no analogue of the correlation coefficient in extreme value theory, and there does not exist an efficient tail independence test statistic, these two new concepts may open up a new field of study. In addition, an alternative to Spearman’s rank correlation, a rank based quotient correlation, is also defined. The advantages of using these new concepts are illustrated with simulated data and a real data analysis of internet traffic.