{"ID":2895206,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2507.09584","arxiv_id":"2507.09584","title":"Edgeworth corrections for the spiked eigenvalues of non-Gaussian sample covariance matrices with applications","abstract":"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.","short_abstract":"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 expans...","url_abs":"https://arxiv.org/abs/2507.09584","url_pdf":"https://arxiv.org/pdf/2507.09584v2","authors":"[\"Yashi Wei\",\"Jiang Hu\",\"Zhidong Bai\"]","published":"2025-07-13T11:36:45Z","proceeding":"math.ST","tasks":"[\"math.ST\",\"math.PR\",\"stat.ME\"]","methods":"[]","has_code":false}