A Review on Correlation Coefficients

Xu Wei-chao

doi:10.3969/j.issn.1007-7162.2012.03.002

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A Review on Correlation Coefficients

更新时间：2026-05-27

- A Review on Correlation Coefficients
- Vol. 29, Issue 3, Pages: 12-17(2012)
- 作者机构：
- 作者简介：
- 基金信息：
- DOI：10.3969/j.issn.1007-7162.2012.03.002
  CLC：
- Online First：20 September 2012，
  
  Published：2012
- 稿件说明：
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徐维超. 相关系数研究综述[J]. 广东工业大学学报, 2012, 29(3): 12-17.

Xu Wei-chao. A Review on Correlation Coefficients[J]. 2012, 29(3): 12-17.
徐维超. 相关系数研究综述[J]. 广东工业大学学报, 2012, 29(3): 12-17. DOI： 10.3969/j.issn.1007-7162.2012.03.002.

Xu Wei-chao. A Review on Correlation Coefficients[J]. 2012, 29(3): 12-17. DOI： 10.3969/j.issn.1007-7162.2012.03.002.

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.

关键词

Keywords

references

Gibbons J D, Chakraborti S. Nonparametric Statistical Inference[M]. 3rd. New York: M Dekker, 1992.

Fisher R A. Statistical Methods, Experimental Design,and Scientific Inference[M]. New York: Oxford UniversityPress, 1990.

Fisher R A. On the ‘probable error’ of a coefficient of correlation deduced from a small sample[J]. Metron, 1921,1:3-32.

Fieller E C, Hartley H O, Pearson E S. Tests for rank correlation coefficients[J]. Biometrika, 1957,44(3/4):470-481.

Kendall M, Gibbons J D. Rank Correlation Methods[M].5th. New York: Oxford University Press, 1990.

Fisher R. Frequency distribution of the values of the correlation coefficient in samples from an indefinitely large population[J]. Biometrika, 1915, 10(4):507-521.

Tumanski S. Principles of Electrical Measurement[M].New York: Taylor & Francis, 2006.

Stein D. Detection of random signals in Gaussian mixture noise[J]. IEEE Trans Inf Theory, 1995,41(6):1788-1801.

Chen R, Wang X, Liu J. Adaptive joint detection and decoding in flat-fading channels via mixture Kalman filtering[J]. IEEE Trans Inf Theory, 2000, 46(6):2079-2094.

Reznic Z, Zamir R, Feder M. Joint source-channel coding of a Gaussian mixture source over the Gaussian broadcast channel[J]. IEEE Trans Inf Theory, 2002,48(3):776-781.

Shevlyakov G L, Vilchevski N O. Robustness in Data Analysis: criteria and methods[M]. Modern probability and statistics. Utrecht: VSP, 2002.

Schechtman E, Yitzhaki S. A measure of association base on Ginis mean difference[J]. Commun Statist-Theor Meth, 1987,16(1):207-231.

Xu W, Chang C, Hung Y S, et al. Order Statistics Correlation Coefficient as a Novel Association Measurement With Applications to Biosignal Analysis[J]. IEEE Trans Signal Process, 2007, 55(12):5552-5563.

Xu W, Chang C, Hung Y S, et al. Asymptotic Properties of Order Statistics Correlation Coefficient in the Normal Cases[J]. IEEE Trans Signal Process, 2008,56(6):2239-2248.

Xu W, Hung Y S, Niranjan M, et al. Asymptotic Mean and Variance of Gini Correlation for Bivariate Normal Samples[J]. IEEE Trans Signal Process, 2010,58(2):522-534.

Mari D D, Kotz S. Correlation and Dependence[M]. London:Imperial College Press, 2001.

Hoeffding W. A Class of Statistics with Asymptotically Normal Distribution[J]. Ann Math Stat, 1948,19(3):293-325.

Daniels H E. The Relation Between Measures of Correlation in the Universe of Sample Permutations[J].Biometrika,1944, 33(2):129-135.

Hotelling H. New light on the correlation coefficient and its transforms[J]. Journal of the Royal Statistical Society, Series B(Methodological), 1953, 15(2):193-232.

Moran P A P. Rank Correlation and Product-Moment Correlation[J]. Biometrika, 1948, 35(1/2):203-206.

Esscher F. On a method of determining correlation from the ranks of the variates[J]. Skand Aktuar, 1924,7:201-219.

David F N, Mallows C L. The variance of Spearmans rho in normal samples[J]. Biometrika, 1961, 48(1/2):19-28.

Stuart A, Ord J K. Kendalls Advanced Theory of Statis-tics: Volume 2 Classical Inference and Relationship[M].5th. London: Edward Arnold, 1991.

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