Division of Biostatistics, University of California, Berkeley, CA 94720, United States.
Department of Biostatistics, University of Michigan, Ann Arbor, MI 48109, United States.
Biometrics. 2024 Mar 27;80(2). doi: 10.1093/biomtc/ujae021.
Brain-effective connectivity analysis quantifies directed influence of one neural element or region over another, and it is of great scientific interest to understand how effective connectivity pattern is affected by variations of subject conditions. Vector autoregression (VAR) is a useful tool for this type of problems. However, there is a paucity of solutions when there is measurement error, when there are multiple subjects, and when the focus is the inference of the transition matrix. In this article, we study the problem of transition matrix inference under the high-dimensional VAR model with measurement error and multiple subjects. We propose a simultaneous testing procedure, with three key components: a modified expectation-maximization (EM) algorithm, a test statistic based on the tensor regression of a bias-corrected estimator of the lagged auto-covariance given the covariates, and a properly thresholded simultaneous test. We establish the uniform consistency for the estimators of our modified EM, and show that the subsequent test achieves both a consistent false discovery control, and its power approaches one asymptotically. We demonstrate the efficacy of our method through both simulations and a brain connectivity study of task-evoked functional magnetic resonance imaging.
脑有效连接分析量化了一个神经元素或区域对另一个神经元素或区域的直接影响，了解有效连接模式如何受到主体条件变化的影响具有重要的科学意义。向量自回归 (VAR) 是解决此类问题的有用工具。然而，当存在测量误差、存在多个主体以及关注转移矩阵的推断时，解决方案就很少了。在本文中，我们研究了具有测量误差和多个主体的高维 VAR 模型中转移矩阵推断的问题。我们提出了一种同时测试程序，具有三个关键组成部分：修改后的期望最大化 (EM) 算法、基于张量回归的测试统计量，该回归基于给定协变量的滞后自协方差的偏置校正估计量，以及适当阈值的同时测试。我们证明了我们的修改后的 EM 估计量的一致性，并表明后续测试实现了一致的假发现控制，并且其功效在渐近时接近 1。我们通过模拟和任务诱发功能磁共振成像的脑连接研究证明了我们方法的有效性。
