IDEAS home Printed from https://ideas.repec.org/a/taf/japsta/v31y2004i2p131-143.html
   My bibliography  Save this article

Inferences Based on a Skipped Correlation Coefficient

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.tandfonline.com/doi/abs/10.1080/0266476032000148821
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/0266476032000148821?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    3. 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.
    4. Peter J. Rousseeuw & Ida Ruts, 1996. "Bivariate Location Depth," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 45(4), pages 516-526, December.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Brandi, Giuseppe & Di Matteo, T., 2022. "Multiscaling and rough volatility: An empirical investigation," International Review of Financial Analysis, Elsevier, vol. 84(C).
    2. Giuseppe Brandi & T. Di Matteo, 2022. "Multiscaling and rough volatility: an empirical investigation," Papers 2201.10466, arXiv.org.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Mia Hubert & Peter Rousseeuw & Pieter Segaert, 2015. "Multivariate functional outlier detection," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 24(2), pages 177-202, July.
    2. Mia Hubert & Peter Rousseeuw & Pieter Segaert, 2017. "Multivariate and functional classification using depth and distance," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 11(3), pages 445-466, September.
    3. Wilcox, Rand R., 2003. "Inferences based on multiple skipped correlations," Computational Statistics & Data Analysis, Elsevier, vol. 44(1-2), pages 223-236, October.
    4. Masse, Jean-Claude & Plante, Jean-Francois, 2003. "A Monte Carlo study of the accuracy and robustness of ten bivariate location estimators," Computational Statistics & Data Analysis, Elsevier, vol. 42(1-2), pages 1-26, February.
    5. Xiaohui Liu & Shihua Luo & Yijun Zuo, 2020. "Some results on the computing of Tukey’s halfspace median," Statistical Papers, Springer, vol. 61(1), pages 303-316, February.
    6. Andrés Ortega-Ballesteros & Francisco Iturriaga-Bustos & Alberto-Jesus Perea-Moreno & David Muñoz-Rodríguez, 2022. "Advanced Pressure Management for Sustainable Leakage Reduction and Service Optimization: A Case Study in Central Chile," Sustainability, MDPI, vol. 14(19), pages 1-16, September.
    7. Zuo, Yijun & Lai, Shaoyong, 2011. "Exact computation of bivariate projection depth and the Stahel-Donoho estimator," Computational Statistics & Data Analysis, Elsevier, vol. 55(3), pages 1173-1179, March.
    8. Fabio Galeotti & Daniel John Zizzo, 2015. "Competence versus Honesty : What Do Voters Care About ?," Working Papers 1520, Groupe d'Analyse et de Théorie Economique Lyon St-Étienne (GATE Lyon St-Étienne), Université de Lyon.
    9. Fabio Galeotti & Daniel John Zizzo, 2014. "Competence versus Trustworthiness: What Do Voters Care About?," Post-Print halshs-02467510, HAL.
    10. repec:cte:wsrepe:28434 is not listed on IDEAS
    11. Aldo Corbellini & Marco Riani & Anthony Atkinson, 2015. "Hubert, Rousseeuw and Segaert: multivariate functional outlier detection," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 24(2), pages 257-261, July.
    12. Chanont Banternghansa & Michael W. McCracken, 2009. "Forecast disagreement among FOMC members," Working Papers 2009-059, Federal Reserve Bank of St. Louis.
    13. Dyckerhoff, Rainer & Mozharovskyi, Pavlo, 2016. "Exact computation of the halfspace depth," Computational Statistics & Data Analysis, Elsevier, vol. 98(C), pages 19-30.
    14. Marc Hallin & Davy Paindaveine & Miroslav Siman, 2008. "Multivariate quantiles and multiple-output regression quantiles: from L1 optimization to halfspace depth," Working Papers ECARES 2008_042, ULB -- Universite Libre de Bruxelles.
    15. Cerioli, Andrea & Farcomeni, Alessio & Riani, Marco, 2014. "Strong consistency and robustness of the Forward Search estimator of multivariate location and scatter," Journal of Multivariate Analysis, Elsevier, vol. 126(C), pages 167-183.
    16. Nolan, D., 1999. "On min-max majority and deepest points," Statistics & Probability Letters, Elsevier, vol. 43(4), pages 325-333, July.
    17. Anthony Atkinson & Marco Riani, 2004. "The forward search and data visualisation," Computational Statistics, Springer, vol. 19(1), pages 29-54, February.
    18. Peter Congdon, 2017. "Quantile regression for overdispersed count data: a hierarchical method," Journal of Statistical Distributions and Applications, Springer, vol. 4(1), pages 1-19, December.
    19. Hamel, Andreas H. & Kostner, Daniel, 2022. "Computation of quantile sets for bivariate ordered data," Computational Statistics & Data Analysis, Elsevier, vol. 169(C).
    20. Xiaohui Liu, 2017. "Fast implementation of the Tukey depth," Computational Statistics, Springer, vol. 32(4), pages 1395-1410, December.
    21. Sara López-Pintado & Ying Sun & Juan Lin & Marc Genton, 2014. "Simplicial band depth for multivariate functional data," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 8(3), pages 321-338, September.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:taf:japsta:v:31:y:2004:i:2:p:131-143. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/CJAS20 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.