On spiked eigenvalues of a renormalized sample covariance matrix from multi-population
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910602558963712 |
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| author | Li, Weiming Li, Zeng Zhu, Junpeng |
| author_facet | Li, Weiming Li, Zeng Zhu, Junpeng |
| contents | Sample covariance matrices from multi-population typically exhibit several large spiked eigenvalues, which stem from differences between population means and are crucial for inference on the underlying data structure. This paper investigates the asymptotic properties of spiked eigenvalues of a renormalized sample covariance matrices from multi-population in the ultrahigh dimensional context where the dimension-to-sample size ratio p/n go to infinity. The first- and second-order convergence of these spikes are established based on asymptotic properties of three types of sesquilinear forms from multi-population. These findings are further applied to two scenarios,including determination of total number of subgroups and a new criterion for evaluating clustering results in the absence of true labels. Additionally, we provide a unified framework with p/n->c\in (0,\infty] that integrates the asymptotic results in both high and ultrahigh dimensional settings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_08715 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On spiked eigenvalues of a renormalized sample covariance matrix from multi-population Li, Weiming Li, Zeng Zhu, Junpeng Statistics Theory Sample covariance matrices from multi-population typically exhibit several large spiked eigenvalues, which stem from differences between population means and are crucial for inference on the underlying data structure. This paper investigates the asymptotic properties of spiked eigenvalues of a renormalized sample covariance matrices from multi-population in the ultrahigh dimensional context where the dimension-to-sample size ratio p/n go to infinity. The first- and second-order convergence of these spikes are established based on asymptotic properties of three types of sesquilinear forms from multi-population. These findings are further applied to two scenarios,including determination of total number of subgroups and a new criterion for evaluating clustering results in the absence of true labels. Additionally, we provide a unified framework with p/n->c\in (0,\infty] that integrates the asymptotic results in both high and ultrahigh dimensional settings. |
| title | On spiked eigenvalues of a renormalized sample covariance matrix from multi-population |
| topic | Statistics Theory |
| url | https://arxiv.org/abs/2409.08715 |