Asymptotic limits of spiked eigenvalues and eigenvectors of signal-plus-noise matrices with weak signals and heteroskedastic noise
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arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866915280674881536 |
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| author | Liu, Xiaoyu Liu, Yiming Pan, Guangming Zhang, Lingyue Zhang, Zhixiang |
| author_facet | Liu, Xiaoyu Liu, Yiming Pan, Guangming Zhang, Lingyue Zhang, Zhixiang |
| contents | This paper is to study a signal-plus-noise model in high dimensional settings when the dimension and the sample size are comparable. Specifically, we assume that the noise has a general covariance matrix that allows for heteroskedasticity, and that the deterministic signal has the same magnitude as the noise and can have a rank that tends to infinity. We develop the asymptotic limits of the left and right spiked singular vectors of the signal-plusnoise data matrix and the limits of the spiked eigenvalues of the corresponding Gram matrix. As an application, we propose a new criterion to estimate the number of clusters in clustering problems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_13939 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Asymptotic limits of spiked eigenvalues and eigenvectors of signal-plus-noise matrices with weak signals and heteroskedastic noise Liu, Xiaoyu Liu, Yiming Pan, Guangming Zhang, Lingyue Zhang, Zhixiang Statistics Theory This paper is to study a signal-plus-noise model in high dimensional settings when the dimension and the sample size are comparable. Specifically, we assume that the noise has a general covariance matrix that allows for heteroskedasticity, and that the deterministic signal has the same magnitude as the noise and can have a rank that tends to infinity. We develop the asymptotic limits of the left and right spiked singular vectors of the signal-plusnoise data matrix and the limits of the spiked eigenvalues of the corresponding Gram matrix. As an application, we propose a new criterion to estimate the number of clusters in clustering problems. |
| title | Asymptotic limits of spiked eigenvalues and eigenvectors of signal-plus-noise matrices with weak signals and heteroskedastic noise |
| topic | Statistics Theory |
| url | https://arxiv.org/abs/2310.13939 |