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Abstract：
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.
摘要：
大脑有效连接分析量化一个神经元或区域对另一个神经元或区域的直接影响，了解有效的连接模式如何受到受试者条件变化的影响具有极大的科学意义。向量自回归（VAR）是解决此类问题的有用工具。然而,当存在测量误差时，解决方案很少，当有多个主题时，当焦点是转移矩阵的推断时。在这篇文章中,研究了具有测量误差和多主体的高维VAR模型下的转移矩阵推断问题。我们提出了一个同时测试程序，具有三个关键组成部分：改进的期望最大化(EM)算法，基于给定协变量的滞后自协方差的偏差校正估计器的张量回归的检验统计量，和适当的阈值同时测试。我们为修改后的EM的估计量建立了统一的一致性，并表明后续测试实现了一致的错误发现控制，它的力量渐近地接近一个。我们通过模拟和任务诱发功能磁共振成像的大脑连通性研究证明了我们方法的有效性。
