The multiple-subject vector autoregression (multi-VAR) model captures heterogeneous network Granger causality across subjects by decomposing individual sparse VAR transition matrices into commonly shared and subject-unique paths. The model has been applied to characterize hidden shared and unique paths among subjects and has demonstrated performance compared to methods commonly used in psychology and neuroscience. Despite this innovation, the model suffers from using a weighted median for identifying the common effects, leading to statistical inefficiency as the convergence rates of the common and unique paths are determined by the least sparse subject and the smallest sample size across all subjects. We propose a new identifiability condition for the multi-VAR model based on a communication-efficient data integration framework. We show that this approach achieves convergence rates tailored to each subject's sparsity level and sample size. Furthermore, we develop hypothesis tests to assess the nullity and homogeneity of individual paths, using Wald-type test statistics constructed from individual debiased estimators. A test for the significance of the common paths can also be derived through the framework. Simulation studies under various heterogeneity scenarios and a real data application demonstrate the performance of the proposed method compared to existing benchmark across standard evaluation metrics.

翻译：多主体向量自回归模型通过将个体稀疏VAR转移矩阵分解为共同共享路径与主体特有路径，捕捉了不同主体间异质的网络格兰杰因果关系。该模型已被应用于刻画主体间隐藏的共享与特有路径，并在与心理学和神经科学常用方法的比较中展现了其性能。尽管具有这一创新性，该模型在识别共同效应时使用了加权中位数方法，导致统计效率低下——因为共同路径与特有路径的收敛速率分别由最不稀疏的主体和所有主体中最小的样本量决定。我们基于一种通信高效的数据集成框架，为多主体VAR模型提出了一种新的可识别性条件。我们证明该方法能够实现适应每个主体稀疏水平与样本量的收敛速率。此外，我们利用由个体去偏估计量构建的Wald型检验统计量，开发了用于评估个体路径的零性与同质性的假设检验。通过该框架亦可推导出针对共同路径显著性的检验。在不同异质性场景下的模拟研究以及实际数据应用表明，相较于现有基准方法，所提方法在标准评估指标上均表现出优越性能。