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arXiv · 2401.12190

Concentration inequalities for the sample correlation coefficient

Daniel Salnikov
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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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Daniel Salnikov. 2024-01-22. Concentration inequalities for the sample correlation coefficient. https://arxiv.org/abs/2401.12190

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