Edgeworth corrections for the spiked eigenvalues of non-Gaussian sample covariance matrices with applications
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909693053501440 |
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| author | Wei, Yashi Hu, Jiang Bai, Zhidong |
| author_facet | Wei, Yashi Hu, Jiang Bai, Zhidong |
| contents | Yang and Johnstone (2018) established an Edgeworth correction for the largest sample eigenvalue in a spiked covariance model under the assumption of Gaussian observations, leaving the extension to non-Gaussian settings as an open problem. In this paper, we address this issue by establishing first-order Edgeworth expansions for spiked eigenvalues in both single-spike and multi-spike scenarios with non-Gaussian data. Leveraging these expansions, we construct more accurate confidence intervals for the population spiked eigenvalues and propose a novel estimator for the number of spikes. Simulation studies demonstrate that our proposed methodology outperforms existing approaches in both robustness and accuracy across a wide range of settings, particularly in low-dimensional cases. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_09584 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Edgeworth corrections for the spiked eigenvalues of non-Gaussian sample covariance matrices with applications Wei, Yashi Hu, Jiang Bai, Zhidong Statistics Theory Probability Methodology Yang and Johnstone (2018) established an Edgeworth correction for the largest sample eigenvalue in a spiked covariance model under the assumption of Gaussian observations, leaving the extension to non-Gaussian settings as an open problem. In this paper, we address this issue by establishing first-order Edgeworth expansions for spiked eigenvalues in both single-spike and multi-spike scenarios with non-Gaussian data. Leveraging these expansions, we construct more accurate confidence intervals for the population spiked eigenvalues and propose a novel estimator for the number of spikes. Simulation studies demonstrate that our proposed methodology outperforms existing approaches in both robustness and accuracy across a wide range of settings, particularly in low-dimensional cases. |
| title | Edgeworth corrections for the spiked eigenvalues of non-Gaussian sample covariance matrices with applications |
| topic | Statistics Theory Probability Methodology |
| url | https://arxiv.org/abs/2507.09584 |