## DIMACS TR: 2001-25

## Remarks on the maximum correlation coefficient

### Authors: Amir Dembo, Abram Kagan, and Lawrence A. Shepp

**
ABSTRACT
**

The maximum correlation coefficient between partial sums
of independent 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. Besides proving this, relations
between
linearity of regression of each of two random variables on the other
and the maximum correlation coefficient are discussed.

Paper Available at:
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