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<p>In this paper, we propose a new corrected likelihood ratio test (LRT) for simultaneously testing mean vectors and covariance matrices of two-sample populations in high-dimensional settings. By employing tools from Random Matrix Theory (RMT), we derive the limiting null distribution of the corrected LRT for generally distributed populations. Furthermore, we compare the proposed test with existing tests using simulation results, demonstrating that the corrected LRT exhibits favorable properties in terms of both size and power.</p>

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Simultaneous test of the mean vectors and covariance matrices for high-dimensional data using RMT

  • 期刊论文

  • 发表日期：

    2026年3月6日

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  • Zhenzhen Niu,
  • Jianghao Li,
  • Wenya Luo,
  • Zhidong Bai

摘要

In this paper, we propose a new corrected likelihood ratio test (LRT) for simultaneously testing mean vectors and covariance matrices of two-sample populations in high-dimensional settings. By employing tools from Random Matrix Theory (RMT), we derive the limiting null distribution of the corrected LRT for generally distributed populations. Furthermore, we compare the proposed test with existing tests using simulation results, demonstrating that the corrected LRT exhibits favorable properties in terms of both size and power.