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<p>In this paper, we consider the phase transition of Wilks’ phenomenon for the likelihood ratio statistic on testing the high-dimensional block compound symmetry covariance structure. When both the sample size and the dimension tend to infinity, we establish the necessary and sufficient condition for Wilks’ phenomenon, and also obtain the asymptotic bias of the chi-squared approximation and the precise expansion of the asymptotic distribution under a local asymptotic regime. Some numerical simulations are shown to illustrate the theoretical results. The results provide practical guidance for testing on high-dimensional block compound symmetry covariance structure.</p>

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On the phase transition of Wilks’ phenomenon under block compound symmetry covariance structure

  • 期刊论文

  • 发表日期：

    2026年6月25日

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  • Ping Tang,
  • Junshan Xie

摘要

In this paper, we consider the phase transition of Wilks’ phenomenon for the likelihood ratio statistic on testing the high-dimensional block compound symmetry covariance structure. When both the sample size and the dimension tend to infinity, we establish the necessary and sufficient condition for Wilks’ phenomenon, and also obtain the asymptotic bias of the chi-squared approximation and the precise expansion of the asymptotic distribution under a local asymptotic regime. Some numerical simulations are shown to illustrate the theoretical results. The results provide practical guidance for testing on high-dimensional block compound symmetry covariance structure.