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Some counterexamples concerning maximal correlation and linear regression

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  • 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
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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. 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.
    3. Eaton, Morris L., 1986. "A characterization of spherical distributions," Journal of Multivariate Analysis, Elsevier, vol. 20(2), pages 272-276, December.
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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. 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.

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