Dimension-free Structured Covariance Estimation
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909224375681024 |
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| author | Puchkin, Nikita Rakhuba, Maxim |
| author_facet | Puchkin, Nikita Rakhuba, Maxim |
| contents | Given a sample of i.i.d. high-dimensional centered random vectors, we consider a problem of estimation of their covariance matrix $Σ$ with an additional assumption that $Σ$ can be represented as a sum of a few Kronecker products of smaller matrices. Under mild conditions, we derive the first non-asymptotic dimension-free high-probability bound on the Frobenius distance between $Σ$ and a widely used penalized permuted least squares estimate. Because of the hidden structure, the established rate of convergence is faster than in the standard covariance estimation problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_10032 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Dimension-free Structured Covariance Estimation Puchkin, Nikita Rakhuba, Maxim Statistics Theory Signal Processing Given a sample of i.i.d. high-dimensional centered random vectors, we consider a problem of estimation of their covariance matrix $Σ$ with an additional assumption that $Σ$ can be represented as a sum of a few Kronecker products of smaller matrices. Under mild conditions, we derive the first non-asymptotic dimension-free high-probability bound on the Frobenius distance between $Σ$ and a widely used penalized permuted least squares estimate. Because of the hidden structure, the established rate of convergence is faster than in the standard covariance estimation problem. |
| title | Dimension-free Structured Covariance Estimation |
| topic | Statistics Theory Signal Processing |
| url | https://arxiv.org/abs/2402.10032 |