2025/05/13 by Jiang, Qianqian, Zhu, Junpeng, Li, Zeng
#FOS: Mathematics #Statistics Theory (math.ST)
paper · doi:10.48550/arxiv.2505.08210
This paper studies the asymptotic spectral properties of a renormalized sample correlation matrix, including the limiting spectral distribution, the properties of largest eigenvalues, and the central limit theorem for linear spectral statistics. All asymptotic results are derived under a unified framework where the dimension-to-sample size ratio p/n→ c∈ (0,∞]. Based on our CLT result, we propose an independence test statistic capable of operating effectively in both high and ultrahigh dimensional scenarios. Simulation experiments demonstrate the accuracy of theoretical results.