The paper considers a high-dimensional likelihood ratio (LR) test on the intraclass correlation structure of the multivariate normal population. When the dimension p and sample size N satisfy N − 1 >p→∞ , it is proved that the logarithmic LR statistic asymptotically obeys Gaussian distribution, and the explicit expressions of the mean and the variance are also obtained. The simulations demonstrate that our high-dimensional LR test method outperforms the traditional Chi-square approximation method or F-approximation method, and performs as efficient as the accurate high-dimensional Edgeworth expansion method and the more accurate high-dimensional Edgeworth expansion method in analyzing the intraclass covariance structure of highdimensional data.

The paper considers a high-dimensional likelihood ratio (LR) test on the intraclass correlation structure of the multivariate normal population. When the dimension p and sample size N satisfy N − 1 >p→∞ , it is proved that the logarithmic LR statistic asymptotically obeys Gaussian distribution, and the explicit expressions of the mean and the variance are also obtained. The simulations demonstrate that our high-dimensional LR test method outperforms the traditional Chi-square approximation method or F-approximation method, and performs as efficient as the accurate high-dimensional Edgeworth expansion method and the more accurate high-dimensional Edgeworth expansion method in analyzing the intraclass covariance structure of highdimensional data.