Edgeworth corrections for the spiked eigenvalues of non-Gaussian sample covariance matrices with applications

2025/07/13 by Jiang Hu, Wei, Yashi, Zhidong Bai +2
Mathematics · #Confidence interval #Covariance #Covariance matrix #Eigenvalues and eigenvectors #Estimator #FOS: Computer and information sciences #FOS: Mathematics #Gaussian #Methodology (stat.ME) #Probability (math.PR) #Random Matrices and Applications #Range (aeronautics) #Robustness (evolution) #Sample mean and sample covariance #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.2507.09584

openalex publication_date 2025/07/13 · openalex created_date 2025/10/18 · openalex updated_date 2026/08/05

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.

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