相关系数研究综述

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doi:10.3969/j.issn.1007-7162.2012.03.002

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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.

Abstract

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 correlation 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.

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references

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