We introduce novel hypothesis testing methods for Gaussian graphical models, whose foundation is an innovative algorithm that generates exchangeable copies from these models. We utilize the exchangeable copies to formulate a goodness-of-fit test, which is valid in both low and high-dimensional settings and flexible in choosing the test statistic. This test exhibits superior power performance, especially in scenarios where the true precision matrix violates the null hypothesis with many small entries. Furthermore, we adapt the sampling algorithm for constructing a new conditional randomization test for the conditional independence between a response $Y$ and a vector of covariates $X$ given some other variables $Z$. Thanks to the model-X framework, this test does not require any modeling assumption about $Y$ and can utilize test statistics from advanced models. It also relaxes the assumptions of conditional randomization tests by allowing the number of unknown parameters of the distribution of $X$ to be much larger than the sample size. For both of our testing procedures, we propose several test statistics and conduct comprehensive simulation studies to demonstrate their superior performance in controlling the Type-I error and achieving high power. The usefulness of our methods is further demonstrated through three real-world applications.

翻译：我们针对高斯图模型提出了一种新颖的假设检验方法，其基础是一种从这些模型中生成可交换副本的创新算法。我们利用可交换副本构建了拟合优度检验，该检验在低维和高维场景下均有效，且检验统计量的选择具有灵活性。这一检验展现出优越的检验功效，尤其是在真实精度矩阵违反原假设且包含大量小数值元素的场景中。此外，我们对该采样算法进行了改进，用于构建一种新的条件随机化检验，以检验给定其他变量$Z$后响应变量$Y$与协变量向量$X$之间的条件独立性。得益于模型-X框架，该检验无需对$Y$建立任何建模假设，且能利用来自先进模型的检验统计量。它还放宽了条件随机化检验的假设条件，允许$X$分布中的未知参数数量远大于样本量。对于上述两种检验流程，我们提出了多种检验统计量，并通过全面的仿真研究证明其在控制第一类错误率和实现高检验功效方面的优越性能。三种实际应用案例进一步验证了所提方法的实用性。