High dimensional convergence rates for sparse precision estimators for matrix-variate data
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866915369553231872 |
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| author | Sun, Hongqiang Khare, Kshitij |
| author_facet | Sun, Hongqiang Khare, Kshitij |
| contents | In several applications, the underlying structure of the data allows for the samples to be organized into a matrix variate form. In such settings, the underlying row and column covariance matrices are fundamental quantities of interest. We focus our attention on two popular estimators that have been proposed in the literature: a penalized sparse estimator called SMGM and a heuristic sample covariance estimator. We establish convergence rates for these estimators in relevant high-dimensional settings, where the row and column dimensions of the matrix are allowed to increase with the sample size. We show that high-dimensional convergence rate analyses for the SMGM estimator in previous literature are incorrect. We discuss the critical errors in these proofs, and present a different and novel approach. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_01741 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | High dimensional convergence rates for sparse precision estimators for matrix-variate data Sun, Hongqiang Khare, Kshitij Statistics Theory 62F12, 62H05 In several applications, the underlying structure of the data allows for the samples to be organized into a matrix variate form. In such settings, the underlying row and column covariance matrices are fundamental quantities of interest. We focus our attention on two popular estimators that have been proposed in the literature: a penalized sparse estimator called SMGM and a heuristic sample covariance estimator. We establish convergence rates for these estimators in relevant high-dimensional settings, where the row and column dimensions of the matrix are allowed to increase with the sample size. We show that high-dimensional convergence rate analyses for the SMGM estimator in previous literature are incorrect. We discuss the critical errors in these proofs, and present a different and novel approach. |
| title | High dimensional convergence rates for sparse precision estimators for matrix-variate data |
| topic | Statistics Theory 62F12, 62H05 |
| url | https://arxiv.org/abs/2507.01741 |