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2025-06-09 08:33:42

On Rank Correlation Coefficients
Alexei Stepanov
https://arxiv.org/abs/2506.06056 https://arxiv.org/pdf/2506.06056

On Rank Correlation Coefficients
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 $ρ_{S,n}$, Kendall $τ_n$ and sample Pearson $ρ_n$ correlation coefficients. Simulation experiments show that when the relationship between $X$ and $Y$ is not close to linear, $r_n$ performs better th…