Remarks on the maximum correlation coefficient

Amir Dembo; Abram Kagan; Lawrence A. Shepp

doi:bj/1080222081

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Home > Journals > Bernoulli > Volume 7 > Issue 2 > Article

April 2001 Remarks on the maximum correlation coefficient

Amir Dembo, Abram Kagan, Lawrence A. Shepp

Author Affiliations +

Amir Dembo,¹ Abram Kagan,² Lawrence A. Shepp³
¹Department of Statistics and Department of Mathematics, Stanford University
²Department of Mathematics, University of Maryland
³Department of Statistics, 501 Hill Center

Bernoulli 7(2): 343-350 (April 2001).

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Abstract

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.