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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2503.18645 |
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| _version_ | 1866915873053212672 |
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| author | Bousseyroux, Pierre Espana, Tomas Smerlak, Matteo |
| author_facet | Bousseyroux, Pierre Espana, Tomas Smerlak, Matteo |
| contents | Bandeira et al. (2017) show that the eigenvalues of the Kendall correlation matrix of $n$ i.i.d. random vectors in $\mathbb{R}^p$ are asymptotically distributed like $1/3 + (2/3)Y_q$, where $Y_q$ has a Marčenko-Pastur law with parameter $q=\lim(p/n)$ if $p, n\to\infty$ proportionately to one another. Here we show that another Marčenko-Pastur law emerges in the "ultra-high dimensional" scaling limit where $p\sim q'\, n^2/2$ for some $q'>0$: in this quadratic scaling regime, Kendall correlation eigenvalues converge weakly almost surely to $(1/3)Y_{q'}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_18645 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Another Marcenko-Pastur law for Kendall's tau Bousseyroux, Pierre Espana, Tomas Smerlak, Matteo Probability Spectral Theory Bandeira et al. (2017) show that the eigenvalues of the Kendall correlation matrix of $n$ i.i.d. random vectors in $\mathbb{R}^p$ are asymptotically distributed like $1/3 + (2/3)Y_q$, where $Y_q$ has a Marčenko-Pastur law with parameter $q=\lim(p/n)$ if $p, n\to\infty$ proportionately to one another. Here we show that another Marčenko-Pastur law emerges in the "ultra-high dimensional" scaling limit where $p\sim q'\, n^2/2$ for some $q'>0$: in this quadratic scaling regime, Kendall correlation eigenvalues converge weakly almost surely to $(1/3)Y_{q'}$. |
| title | Another Marcenko-Pastur law for Kendall's tau |
| topic | Probability Spectral Theory |
| url | https://arxiv.org/abs/2503.18645 |