Concentration inequalities for the sample correlation coefficient
arXiv:2401.12190
Abstract
The sample correlation coefficient plays an important role in many statistical analyses. We study the moments of under the bivariate Gaussian model assumption, provide a novel approximation for its finite sample mean and connect it with known results for the variance. We exploit these approximations to present non-asymptotic concentration inequalities for . Finally, we illustrate our results in a simulation experiment that further validates the approximations presented in this work.
10 pages, preprint