Upper bounds for singular subspaces under unitarily invariant norms with applications to high-dimensional covariance matrix estimation
UDC 519.21, 517.98, 512.64 In [J. Cape, et al., Ann. Statist., 47, Article 2405 (2019)], the authors established perturbation bounds for the $\ell_{2 \to \infty}$-norm of singular subspaces and applied this framework to high-dimensional covariance matrix estimation under multivariate normal distrib...
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| Datum: | 2026 |
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| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
2026
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/8760 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| Zusammenfassung: | UDC 519.21, 517.98, 512.64
In [J. Cape, et al., Ann. Statist., 47, Article 2405 (2019)], the authors established perturbation bounds for the $\ell_{2 \to \infty}$-norm of singular subspaces and applied this framework to high-dimensional covariance matrix estimation under multivariate normal distributions. We establish perturbation bounds for unitarily invariant norms and apply these bounds to multivariate normal and sub-Gaussian random vectors. Combined with our upper bounds, these results enable us to get the improved estimation of high-dimensional covariance matrices. Finally, we perform simulation experiments demonstrating the improved scaling behavior as compared to Cape, et al.'s bounds in the presented experiments. |
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| DOI: | 10.3842/umzh.v78i5-6.8760 |