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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2506.06056 |
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| _version_ | 1866912418742927360 |
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| author | Stepanov, Alexei |
| author_facet | Stepanov, Alexei |
| contents | 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 than other correlation coefficients. We also find analytically the values of $Var(τ_n)$ and $Var(r_n)$. This allows to estimate theoretically the asymptotic performance of $τ_n$ and $r_n$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_06056 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Rank Correlation Coefficients Stepanov, Alexei Statistics Theory G.3 G.3 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 than other correlation coefficients. We also find analytically the values of $Var(τ_n)$ and $Var(r_n)$. This allows to estimate theoretically the asymptotic performance of $τ_n$ and $r_n$. |
| title | On Rank Correlation Coefficients |
| topic | Statistics Theory G.3 G.3 |
| url | https://arxiv.org/abs/2506.06056 |