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April 2001 Remarks on the maximum correlation coefficient
Amir Dembo, Abram Kagan, Lawrence A. Shepp
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Bernoulli 7(2): 343-350 (April 2001).


The maximum correlation coefficient between partial sums of independent and identically distributed random variables with finite second moment equals the classical (Pearson) correlation coefficient between the sums, and thus does not depend on the distribution of the random variables. This result is proved, and relations between the linearity of regression of each of two random variables on the other and the maximum correlation coefficient are discussed.


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Amir Dembo. Abram Kagan. Lawrence A. Shepp. "Remarks on the maximum correlation coefficient." Bernoulli 7 (2) 343 - 350, April 2001.


Published: April 2001
First available in Project Euclid: 25 March 2004

zbMATH: 0981.62051
MathSciNet: MR1828509

Keywords: Correlation , Linear regression , maximum correlation , spherically symmetric distributions , Sums of independent random variables

Rights: Copyright © 2001 Bernoulli Society for Mathematical Statistics and Probability


Vol.7 • No. 2 • April 2001
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