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Non-parametric confidence intervals for covariance and correlation

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  • Christopher Withers
  • Saralees Nadarajah

Abstract

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 $$z$$ z -transformation may be quite inappropriate. Copyright Sapienza Università di Roma 2014

Suggested Citation

  • Christopher Withers & Saralees Nadarajah, 2014. "Non-parametric confidence intervals for covariance and correlation," METRON, Springer;Sapienza Università di Roma, vol. 72(3), pages 283-306, October.
    • Handle: RePEc:spr:metron:v:72:y:2014:i:3:p:283-306
    DOI: 10.1007/s40300-013-0033-9
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    References listed on IDEAS

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    1. Ying Guo & Amita K. Manatunga, 2007. "Nonparametric Estimation of the Concordance Correlation Coefficient under Univariate Censoring," Biometrics, The International Biometric Society, vol. 63(1), pages 164-172, March.
    2. Yehua Li, 2011. "Efficient semiparametric regression for longitudinal data with nonparametric covariance estimation," Biometrika, Biometrika Trust, vol. 98(2), pages 355-370.
    3. Yunling Du, 2003. "Nonparametric analysis of covariance for censored data," Biometrika, Biometrika Trust, vol. 90(2), pages 269-287, June.
    4. Zhijie Xiao & Oliver Linton, 2002. "A Nonparametric Prewhitened Covariance Estimator," Journal of Time Series Analysis, Wiley Blackwell, vol. 23(2), pages 215-250, March.
    5. Wei Biao Wu, 2003. "Nonparametric estimation of large covariance matrices of longitudinal data," Biometrika, Biometrika Trust, vol. 90(4), pages 831-844, December.
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