, Volume 72, Issue 3, pp 283–306 | Cite as

Non-parametric confidence intervals for covariance and correlation

  • Christopher S. Withers
  • Saralees NadarajahEmail author


Consider a sample of independent and identical bivariate observations. Simple consistent confidence intervals for the variances, covariance, and correlation of the underlying population are obtained from their influence functions. They contrast with their confidence intervals obtained under the assumption of normality, which are shown to be not consistent if the assumption of normality is false. Even when the marginals are normal, we show that Fisher’s \(z\)-transformation may be quite inappropriate.


Confidence interval Correlation Covariance Influence function 



The authors would like to thank the Editor and the referee for careful reading and for their comments which greatly improved the paper.


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Copyright information

© Sapienza Università di Roma 2014

Authors and Affiliations

  1. 1.Applied Mathematics GroupIndustrial Research LimitedLower HuttNew Zealand
  2. 2.School of MathematicsUniversity of ManchesterManchesterUK

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