IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v126y2014icp114-117.html
   My bibliography  Save this article

Some counterexamples concerning maximal correlation and linear regression

Author

Listed:
  • Papadatos, Nickos

Abstract

A class of examples concerning the relationship of linear regression and maximal correlation is provided. More precisely, these examples show that if two random variables have (strictly) linear regression on each other, then their maximal correlation is not necessarily equal to their (absolute) correlation.

Suggested Citation

  • Papadatos, Nickos, 2014. "Some counterexamples concerning maximal correlation and linear regression," Journal of Multivariate Analysis, Elsevier, vol. 126(C), pages 114-117.
    • Handle: RePEc:eee:jmvana:v:126:y:2014:i:c:p:114-117
    DOI: 10.1016/j.jmva.2013.12.008
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X13002686
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2013.12.008?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. Papadatos, Nickos & Xifara, Tatiana, 2013. "A simple method for obtaining the maximal correlation coefficient and related characterizations," Journal of Multivariate Analysis, Elsevier, vol. 118(C), pages 102-114.
    2. Angelo Koudou, 1998. "Lancaster bivariate probability distributions with Poisson, negative binomial and gamma margins," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 7(1), pages 95-110, June.
    3. Eaton, Morris L., 1986. "A characterization of spherical distributions," Journal of Multivariate Analysis, Elsevier, vol. 20(2), pages 272-276, 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. Tamás F. Móri & Gábor J. Székely, 2019. "Four simple axioms of dependence measures," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 82(1), pages 1-16, January.
    2. López Blázquez, F. & Salamanca Miño, B., 2014. "Maximal correlation in a non-diagonal case," Journal of Multivariate Analysis, Elsevier, vol. 131(C), pages 265-278.

    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. Hugo Brango & Angie Guerrero & Humberto Llinás, 2024. "Marshall–Olkin Bivariate Weibull Model with Modified Singularity (MOBW- μ ): A Study of Its Properties and Correlation Structure," Mathematics, MDPI, vol. 12(14), pages 1-16, July.
    2. Tamás F. Móri & Gábor J. Székely, 2019. "Four simple axioms of dependence measures," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 82(1), pages 1-16, January.
    3. Strobl Eric V. & Visweswaran Shyam, 2016. "Markov Boundary Discovery with Ridge Regularized Linear Models," Journal of Causal Inference, De Gruyter, vol. 4(1), pages 31-48, March.
    4. Wang, Qin & Xue, Yuan, 2021. "An ensemble of inverse moment estimators for sufficient dimension reduction," Computational Statistics & Data Analysis, Elsevier, vol. 161(C).
    5. Kariya, Takeaki & Kurata, Hiroshi, 2002. "A Maximal Extension of the Gauss-Markov Theorem and Its Nonlinear Version," Journal of Multivariate Analysis, Elsevier, vol. 83(1), pages 37-55, October.
    6. López Blázquez, F. & Salamanca Miño, B., 2014. "Maximal correlation in a non-diagonal case," Journal of Multivariate Analysis, Elsevier, vol. 131(C), pages 265-278.
    7. Cuadras, Carles M. & Greenacre, Michael, 2022. "A short history of statistical association: From correlation to correspondence analysis to copulas," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    8. Wenbin Lu & Lexin Li, 2011. "Sufficient Dimension Reduction for Censored Regressions," Biometrics, The International Biometric Society, vol. 67(2), pages 513-523, June.
    9. Portier, François & Delyon, Bernard, 2013. "Optimal transformation: A new approach for covering the central subspace," Journal of Multivariate Analysis, Elsevier, vol. 115(C), pages 84-107.
    10. Gannoun, Ali & Girard, Stephane & Guinot, Christiane & Saracco, Jerome, 2004. "Sliced inverse regression in reference curves estimation," Computational Statistics & Data Analysis, Elsevier, vol. 46(1), pages 103-122, May.
    11. Dueck, Johannes & Edelmann, Dominic & Richards, Donald, 2017. "Distance correlation coefficients for Lancaster distributions," Journal of Multivariate Analysis, Elsevier, vol. 154(C), pages 19-39.
    12. Fernando López-Blázquez & Begoña Salamanca-Miño, 2021. "Automatic differentiation and maximal correlation of order statistics from discrete parents," Computational Statistics, Springer, vol. 36(4), pages 2889-2915, December.
    13. Alessandro Barbarino & Efstathia Bura, 2017. "A Unified Framework for Dimension Reduction in Forecasting," Finance and Economics Discussion Series 2017-004, Board of Governors of the Federal Reserve System (U.S.).
    14. Li, Lexin & Dennis Cook, R. & Nachtsheim, Christopher J., 2004. "Cluster-based estimation for sufficient dimension reduction," Computational Statistics & Data Analysis, Elsevier, vol. 47(1), pages 175-193, August.
    15. Heng-Hui Lue & Bing-Ran You, 2013. "High-dimensional regression analysis with treatment comparisons," Computational Statistics, Springer, vol. 28(3), pages 1299-1317, June.
    16. Xiangrong Yin & R. Dennis Cook, 2002. "Dimension reduction for the conditional kth moment in regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(2), pages 159-175, May.
    17. Albisetti, Isaia & Balabdaoui, Fadoua & Holzmann, Hajo, 2020. "Testing for spherical and elliptical symmetry," Journal of Multivariate Analysis, Elsevier, vol. 180(C).
    18. Soale, Abdul-Nasah, 2023. "Projection expectile regression for sufficient dimension reduction," Computational Statistics & Data Analysis, Elsevier, vol. 180(C).
    19. Heng-Hui Lue, 2015. "An Inverse-regression Method of Dependent Variable Transformation for Dimension Reduction with Non-linear Confounding," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(3), pages 760-774, September.
    20. Alessandro Barbarino & Efstathia Bura, 2015. "Forecasting with Sufficient Dimension Reductions," Finance and Economics Discussion Series 2015-74, Board of Governors of the Federal Reserve System (U.S.).

    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:eee:jmvana:v:126:y:2014:i:c:p:114-117. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    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.