Concentration inequalities for the sample correlation coefficient
Abstract
The sample correlation coefficient R plays an important role in many statistical analyses. We study the moments of R 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 R. Finally, we illustrate our results in a simulation experiment that further validates the approximations presented in this work.
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