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.
Publié le : 2001-04-14
Classification:
correlation,
linear regression,
maximum correlation,
spherically symmetric distributions,
sums of independent random variables
@article{1080222081,
author = {Dembo, Amir and Kagan, Abram and Shepp, Lawrence A.},
title = {Remarks on the maximum correlation coefficient},
journal = {Bernoulli},
volume = {7},
number = {6},
year = {2001},
pages = { 343-350},
language = {en},
url = {http://dml.mathdoc.fr/item/1080222081}
}
Dembo, Amir; Kagan, Abram; Shepp, Lawrence A. Remarks on the maximum correlation coefficient. Bernoulli, Tome 7 (2001) no. 6, pp. 343-350. http://gdmltest.u-ga.fr/item/1080222081/