Localization Estimator for High Dimensional Tensor Covariance Matrices
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866911368262713344 |
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| author | Sun, Hao-Xuan Chen, Song Xi Qiu, Yumou |
| author_facet | Sun, Hao-Xuan Chen, Song Xi Qiu, Yumou |
| contents | This paper considers covariance matrix estimation of tensor data under high dimensionality. A multi-bandable covariance class is established to accommodate the need for complex covariance structures of multi-layer lattices and general covariance decay patterns. We propose a high dimensional covariance localization estimator for tensor data, which regulates the sample covariance matrix through a localization function. The statistical properties of the proposed estimator are studied by deriving the minimax rates of convergence under the spectral and the Frobenius norms. Numerical experiments and real data analysis on ocean eddy data are carried out to illustrate the utility of the proposed method in practice. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_06989 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Localization Estimator for High Dimensional Tensor Covariance Matrices Sun, Hao-Xuan Chen, Song Xi Qiu, Yumou Methodology 62H12 This paper considers covariance matrix estimation of tensor data under high dimensionality. A multi-bandable covariance class is established to accommodate the need for complex covariance structures of multi-layer lattices and general covariance decay patterns. We propose a high dimensional covariance localization estimator for tensor data, which regulates the sample covariance matrix through a localization function. The statistical properties of the proposed estimator are studied by deriving the minimax rates of convergence under the spectral and the Frobenius norms. Numerical experiments and real data analysis on ocean eddy data are carried out to illustrate the utility of the proposed method in practice. |
| title | Localization Estimator for High Dimensional Tensor Covariance Matrices |
| topic | Methodology 62H12 |
| url | https://arxiv.org/abs/2601.06989 |