On Rank Correlation Coefficients

Alexei Stepanov

paper

On Rank Correlation Coefficients

arXiv:2506.06056

Abstract

In the present paper, we propose a new rank correlation coefficient $r_{n}$ , which is a sample analogue of the theoretical correlation coefficient $r$ , which, in turn, was proposed in the recent work of Stepanov (2025b). We discuss the properties of $r_{n}$ and compare $r_{n}$ with known rank Spearman $I ¨ _{S, n}$ , Kendall $I ¨ _{n}$ and sample Pearson $I ¨ _{n}$ correlation coefficients. Simulation experiments show that when the relationship between $X$ and $Y$ is not close to linear, $r_{n}$ performs better than other correlation coefficients. We also find analytically the values of $V a r (I ¨ _{n})$ and $V a r (r_{n})$ . This allows to estimate theoretically the asymptotic performance of $I ¨ _{n}$ and $r_{n}$ .

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