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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| Дата: | 2026 |
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| Автори: | , , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
2026
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| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/8760 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
Репозитарії
Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1866663701030895616 |
|---|---|
| author | Ren, Chunguang Zhang, Pei Huang, Shiguo Ren, Chunguang Zhang, Pei Huang, Shiguo |
| author_facet | Ren, Chunguang Zhang, Pei Huang, Shiguo Ren, Chunguang Zhang, Pei Huang, Shiguo |
| author_institution_txt_mv | [
{
"author": "Chunguang Ren",
"institution": "School of Mathematics and Information Science, Zhengzhou University of Light Industry, Zhengzhou, China"
},
{
"author": "Pei Zhang",
"institution": "School of Mathematics and Information Science, Zhengzhou University of Light Industry, Zhengzhou, China"
},
{
"author": "Shiguo Huang",
"institution": "School of Mathematics and Information Science, Zhengzhou University of Light Industry, Zhengzhou, China"
}
] |
| author_sort | Ren, Chunguang |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2026-05-30T12:46:19Z |
| description | 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. |
| doi_str_mv | 10.3842/umzh.v78i5-6.8760 |
| first_indexed | 2026-05-30T01:00:42Z |
| format | Article |
| fulltext | |
| id | umjimathkievua-article-8760 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-05-31T01:00:29Z |
| publishDate | 2026 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | |
| spelling | umjimathkievua-article-87602026-05-30T12:46:19Z Upper bounds for singular subspaces under unitarily invariant norms with applications to high-dimensional covariance matrix estimation Upper bounds for singular subspaces under unitarily invariant norms with applications to high-dimensional covariance matrix estimation Ren, Chunguang Zhang, Pei Huang, Shiguo Ren, Chunguang Zhang, Pei Huang, Shiguo Upper bounds, Singular subspace, Unitarily invariant norm, Covariance matrix 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. УДК 519.21, 517.98, 512.64 Верхні межі для сингулярних підпросторів в унітарно-інваріантних нормах та їхнє застосування до оцінювання коваріаційних матриць високої розмірності У роботі Дж. Кейпа та ін. [J. Cape, et al., Ann. Statist., 47, Article 2405 (2019)] отримано межі збурень для $\ell_{2 \to \infty}$-норми сингулярних підпросторів і застосовано їх до задачі оцінювання коваріаційних матриць високої розмірності для багатовимірних нормальних розподілів. У цій статті отримано межі збурень для унітарно-інваріантних норм і застосовано їх до багатовимірних нормальних і субгауссових випадкових векторів. Разом із отриманими верхніми межами ці результати дали змогу покращити оцінки для коваріаційних матриць високої розмірності. Насамкінець проведено числові експерименти, які продемонстрували кращу масштабованість результатів у наведених експериментах порівняно з оцінками Кейпа та ін. Institute of Mathematics, NAS of Ukraine 2026-05-29 Article Article https://umj.imath.kiev.ua/index.php/umj/article/view/8760 10.3842/umzh.v78i5-6.8760 Ukrains’kyi Matematychnyi Zhurnal; Vol. 78 No. 5-6 (2026); 377–378 Український математичний журнал; Том 78 № 5-6 (2026); 377–378 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/8760/10662 Copyright (c) 2026 Chunguang Ren, Pei Zhang, Shiguo Huang |
| spellingShingle | Ren, Chunguang Zhang, Pei Huang, Shiguo Ren, Chunguang Zhang, Pei Huang, Shiguo Upper bounds for singular subspaces under unitarily invariant norms with applications to high-dimensional covariance matrix estimation |
| title | Upper bounds for singular subspaces under unitarily invariant norms with applications to high-dimensional covariance matrix estimation |
| title_alt | Upper bounds for singular subspaces under unitarily invariant norms with applications to high-dimensional covariance matrix estimation |
| title_full | Upper bounds for singular subspaces under unitarily invariant norms with applications to high-dimensional covariance matrix estimation |
| title_fullStr | Upper bounds for singular subspaces under unitarily invariant norms with applications to high-dimensional covariance matrix estimation |
| title_full_unstemmed | Upper bounds for singular subspaces under unitarily invariant norms with applications to high-dimensional covariance matrix estimation |
| title_short | Upper bounds for singular subspaces under unitarily invariant norms with applications to high-dimensional covariance matrix estimation |
| title_sort | upper bounds for singular subspaces under unitarily invariant norms with applications to high-dimensional covariance matrix estimation |
| topic_facet | Upper bounds Singular subspace Unitarily invariant norm Covariance matrix |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/8760 |
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