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Inferences Based on a Skipped Correlation Coefficient

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  • Rand Wilcox

Abstract

The most popular method for trying to detect an association between two random variables is to test H0 : ρ=0, the hypothesis that Pearson's correlation is equal to zero. It is well known, however, that Pearson's correlation is not robust, roughly meaning that small changes in any distribution, including any bivariate normal distribution as a special case, can alter its value. Moreover, the usual estimate of ρ, r, is sensitive to only a few outliers which can mask a true association. A simple alternative to testing H0 : ρ =0 is to switch to a measure of association that guards against outliers among the marginal distributions such as Kendall's tau, Spearman's rho, a Winsorized correlation, or a so-called percentage bend correlation. But it is known that these methods fail to take into account the overall structure of the data. Many measures of association that do take into account the overall structure of the data have been proposed, but it seems that nothing is known about how they might be used to detect dependence. One such measure of association is selected, which is designed so that under bivariate normality, its estimator gives a reasonably accurate estimate of ρ. Then methods for testing the hypothesis of a zero correlation are studied.

Suggested Citation

  • Rand Wilcox, 2004. "Inferences Based on a Skipped Correlation Coefficient," Journal of Applied Statistics, Taylor & Francis Journals, vol. 31(2), pages 131-143.
    • Handle: RePEc:taf:japsta:v:31:y:2004:i:2:p:131-143
    DOI: 10.1080/0266476032000148821
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    References listed on IDEAS

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    1. Carling, Kenneth, 2000. "Resistant outlier rules and the non-Gaussian case," Computational Statistics & Data Analysis, Elsevier, vol. 33(3), pages 249-258, May.
    2. Struyf, Anja & Rousseeuw, Peter J., 2000. "High-dimensional computation of the deepest location," Computational Statistics & Data Analysis, Elsevier, vol. 34(4), pages 415-426, October.
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    4. Zani, Sergio & Riani, Marco & Corbellini, Aldo, 1998. "Robust bivariate boxplots and multiple outlier detection," Computational Statistics & Data Analysis, Elsevier, vol. 28(3), pages 257-270, September.
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    2. Giuseppe Brandi & T. Di Matteo, 2022. "Multiscaling and rough volatility: an empirical investigation," Papers 2201.10466, arXiv.org.

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