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arXiv · 2505.08210

On eigenvalues of a renormalized sample correlation matrix

Qianqian Jiang·Junpeng Zhu·Zeng Li
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Abstract

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 $p/n\rightarrow c\in (0,\infty]$. 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.

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Qianqian Jiang, Junpeng Zhu, Zeng Li. 2025-05-13. On eigenvalues of a renormalized sample correlation matrix. https://arxiv.org/abs/2505.08210

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