Exact test theory in Gaussian graphical models
推导了关于精度矩阵的统计检验，用于确定无向高斯图的结构，给出了检验统计量在零假设下的精确分布和在高维情形下的渐近分布，并通过模拟研究评估了性能。
In this paper, we derive several statistical tests on the precision matrix with application to the determination of the structure of an undirected Gaussian graph. The exact distributions of the test statistics are obtained under the null hypotheses, while the exact distributions of the random matrices, which are used in the construction of the test statistics, are deduced under the alternative hypothesis. Moreover, we present the high-dimensional asymptotic distributions of the test statistics under the null hypothesis. The testing problems that an undirected Gaussian graph possesses a structure that corresponds to the precision matrix of an AR(1) process, to the block-diagonal precision matrix and to the precision of a factor model are discussed in detail. The performance of the proposed statistical tests is further investigated via an extensive simulation study and compared to the benchmark approach.