Kendall Correlation Coefficient for non-Identically Distributed Variables
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arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866908914581241856 |
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| author | Stepanov, Alexei |
| author_facet | Stepanov, Alexei |
| contents | In the present paper, we discuss for the first time the theoretical Kendall correlation coefficient for non-identical bivariate data. In the non-identical case, we first introduce a theoretical Kendall correlation coefficient $τ_n$ and show that the expected value of the rank Kendall correlation coefficient $\tildeτ_n$ is equal to $τ_n$. We then prove that $\tildeτ_n$ converges in probability to $τ=\lim_{n\rightarrow\infty} τ_n$. These facts enable us to state that $τ_n$ is a correctly defined theoretical Kendall correlation coefficient for the non-identical case. We also support our theoretical results by simulation experiments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_25055 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Kendall Correlation Coefficient for non-Identically Distributed Variables Stepanov, Alexei Statistics Theory In the present paper, we discuss for the first time the theoretical Kendall correlation coefficient for non-identical bivariate data. In the non-identical case, we first introduce a theoretical Kendall correlation coefficient $τ_n$ and show that the expected value of the rank Kendall correlation coefficient $\tildeτ_n$ is equal to $τ_n$. We then prove that $\tildeτ_n$ converges in probability to $τ=\lim_{n\rightarrow\infty} τ_n$. These facts enable us to state that $τ_n$ is a correctly defined theoretical Kendall correlation coefficient for the non-identical case. We also support our theoretical results by simulation experiments. |
| title | Kendall Correlation Coefficient for non-Identically Distributed Variables |
| topic | Statistics Theory |
| url | https://arxiv.org/abs/2603.25055 |