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A simple method for obtaining the maximal correlation coefficient and related characterizations

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  • Papadatos, Nickos
  • Xifara, Tatiana

Abstract

We provide a method that enables the simple calculation of the maximal correlation coefficient of a bivariate distribution, under suitable conditions. In particular, the method readily applies to known results on order statistics and records. As an application we provide a new characterization of the exponential distribution: Under a splitting model on independent identically distributed observations, it is the (unique, up to a location-scale transformation) parent distribution that maximizes the correlation coefficient between the records among two different branches of the splitting sequence.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:118:y:2013:i:c:p:102-114
    DOI: 10.1016/j.jmva.2013.03.017
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    References listed on IDEAS

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    1. 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.
    2. Yu, Yaming, 2008. "On the maximal correlation coefficient," Statistics & Probability Letters, Elsevier, vol. 78(9), pages 1072-1075, July.
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    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. 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.
    3. 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).
    4. 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.
    5. 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.
    6. Papadatos, Nickos, 2014. "Some counterexamples concerning maximal correlation and linear regression," Journal of Multivariate Analysis, Elsevier, vol. 126(C), pages 114-117.

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