The paper introduces a new test for testing structures of covariances for high dimensional vectors and the data dimension can be much larger than the sample size. Under proper normalization, central and noncentral limit theorems are established. The asymptotic theory is attained without imposing any explicit restriction between data dimension and sample size. To facilitate the related statistical inference, we propose the balanced Rademacher weighted differencing scheme, which is also the delete-half jackknife, to approximate the distribution of the proposed test statistics. We also develop a new testing procedure for substructures of precision matrices. The simulation results show that the tests outperform the exiting methods both in terms of size and power. Our test procedure is applied to a colorectal cancer dataset.

中文翻译：

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测试高维协方差矩阵

本文介绍了一种用于测试高维向量协方差结构的新测试，数据维可以比样本大小大得多。在适当的归一化下，建立中心和非中心极限定理。无需在数据维数和样本量之间施加任何明确的限制即可获得渐近理论。为了便于进行相关的统计推断，我们提出了一种平衡的Rademacher加权差分方案（也称为删除半折刀），以近似于所提出的检验统计量的分布。我们还为精密矩阵的子结构开发了一种新的测试程序。仿真结果表明，在尺寸和功耗方面，测试均优于现有方法。我们的测试程序适用于大肠癌数据集。