Tensor Elliptical Graphic Model
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908475200634880 |
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| author | Liu, Jixuan Lu, Zhengke Zhou, Le Feng, Long Wang, Zhaojun |
| author_facet | Liu, Jixuan Lu, Zhengke Zhou, Le Feng, Long Wang, Zhaojun |
| contents | We address the problem of robust estimation of sparse high dimensional tensor elliptical graphical model. Most of the research focus on tensor graphical model under normality. To extend the tensor graphical model to more heavy-tailed scenarios, motivated by the fact that up to a constant, the spatial-sign covariance matrix can approximate the true covariance matrix when the dimension turns to infinity under tensor elliptical distribution, we proposed a spatial-sign-based estimator to robustly estimate tensor elliptical graphical model, the rate of which matches the existing rate under normality for a wider family of distribution, i.e. elliptical distribution. We also conducted extensive simulations and real data applications to illustrate the practical utility of the proposed methods, especially under heavy-tailed distribution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_00333 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Tensor Elliptical Graphic Model Liu, Jixuan Lu, Zhengke Zhou, Le Feng, Long Wang, Zhaojun Methodology We address the problem of robust estimation of sparse high dimensional tensor elliptical graphical model. Most of the research focus on tensor graphical model under normality. To extend the tensor graphical model to more heavy-tailed scenarios, motivated by the fact that up to a constant, the spatial-sign covariance matrix can approximate the true covariance matrix when the dimension turns to infinity under tensor elliptical distribution, we proposed a spatial-sign-based estimator to robustly estimate tensor elliptical graphical model, the rate of which matches the existing rate under normality for a wider family of distribution, i.e. elliptical distribution. We also conducted extensive simulations and real data applications to illustrate the practical utility of the proposed methods, especially under heavy-tailed distribution. |
| title | Tensor Elliptical Graphic Model |
| topic | Methodology |
| url | https://arxiv.org/abs/2508.00333 |