相关系数研究综述  

A Review on Correlation Coefficients

作　　者：徐维超[1] 

机构地区：[1]广东工业大学自动化学院,广东广州510006

出　　处：《广东工业大学学报》2012年第3期12-17,共6页Journal of Guangdong University of Technology

基　　金：广东省高等学校人才引进专项资金资助项目(2050205)

摘　　要：相关系数是表征两个随机变量之间统计关系强弱的统计量,在几乎所有科学与技术领域都获得了广泛应用.本文以二元高斯分布为基本模型,对文献中常见的5种相关系数的统计特性作相对全面的回顾与总结,并探讨了其适用的场合.具体结论如下:(1)当样本满足二元高斯分布时,皮尔逊积距相关系数是最佳选择;(2)当样本中存在轻微的单调非线性畸变时,序统计量相关系数比较适用;(3)当样本中存在严重的单调非线性畸变时,斯皮尔曼秩次相关系数或肯德尔秩次相关系数是合适的选择;(4)当只有一路信号中存在单调非线性畸变时,基尼相关是最佳选择;(5)当样本中存在脉冲干扰时,斯皮尔曼秩次相关系数或肯德尔秩次相关系数是合适的选择.As statistics characterizing the strength of statistical relationship between two random variables, correlation coefficients have found wide applications in nearly all science and technology fields. This paper attempts to provide a detailed review on 5 commonly used eorrelation coeffcients in the literature, including a relatively detailed discussion on their statistical properties under the fundamental bivariate normal model and their suitable application scenarios. Specifically, （ 1 ） if the sample follows normal distribution, then the Pearson＇s Product Moment Correlation Coefficient is optimal ; （2） if the monotone nonlinear distortion in the sample is small, then the Order Statistics Correlation Coefficient should be used ; （ 3 ） if the monotone nonlinear distortion in the sample is severe, then the Spearman＇s rho or Kendall＇s tau are feasible;（4） if only one channel is distorted by monotone nonlinearity, then the Gini Correlation is best choice ; and （5） if there exsits impulsive noise in the sample, then the Spearman＇s rho or Kendall＇s tau should be employed.

关 键 词：皮尔逊积距相关系数 斯皮尔曼秩次相关系数 肯德尔秩次相关系数 序统计量相关系数 基尼相关 二元高斯分布 脉冲噪声 

分 类 号：O212.4[理学—概率论与数理统计] O211.5[理学—数学]