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<p>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 <i>p/n</i> → <i>c</i> ∈ (0, ∞]. Based on our central limit theorem result, we propose an independence test statistic capable of operating effectively in both high- and ultrahigh-dimensional scenarios. Simulation experiments demonstrate the accuracy of the theoretical results.</p>

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On eigenvalues of a renormalized sample correlation matrix

  • 期刊论文

  • 发表日期：

    2026年7月30日

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  • Qianqian Jiang,
  • Junpeng Zhu,
  • Zeng Li

摘要

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 central limit theorem result, we propose an independence test statistic capable of operating effectively in both high- and ultrahigh-dimensional scenarios. Simulation experiments demonstrate the accuracy of the theoretical results.