Asymptotics of ultra-high-dimensional generalized spiked sample covariance matrix
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866908999851442176 |
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| author | Seo, Wonjun |
| author_facet | Seo, Wonjun |
| contents | This paper investigates the asymptotics of eigenstructure of sample covariance matrix under the spiked covariance matrix model in ultra-high-dimensional settings, where the dimensionality can grow much faster than the sample size with $ p \asymp n^α $, $ α> 1 $. We establish the first-order convergence limits of eigenvalue locations and eigenvector projections of properly scaled sample covariance matrix. Our results are extensions of \cite{bloemendal16,ding21}. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_26178 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Asymptotics of ultra-high-dimensional generalized spiked sample covariance matrix Seo, Wonjun Statistics Theory This paper investigates the asymptotics of eigenstructure of sample covariance matrix under the spiked covariance matrix model in ultra-high-dimensional settings, where the dimensionality can grow much faster than the sample size with $ p \asymp n^α $, $ α> 1 $. We establish the first-order convergence limits of eigenvalue locations and eigenvector projections of properly scaled sample covariance matrix. Our results are extensions of \cite{bloemendal16,ding21}. |
| title | Asymptotics of ultra-high-dimensional generalized spiked sample covariance matrix |
| topic | Statistics Theory |
| url | https://arxiv.org/abs/2604.26178 |