AI 中文总结
针对网络依赖型高维随机向量，本文提出新型推断方法，建立高斯近似结果与HAC协方差估计器，模拟验证其性能，应用于分析溢出效应随网络同质性指数的变化，揭示低维推断未发现的异质性与局部显著性。
AI 中文摘要
我们开发了一种针对网络依赖型高维随机向量的新型推断方法。该方法通过基于图距离的函数依赖度来刻画依赖性，使近似理论能够捕捉依赖衰减与网络邻域增长之间的相互作用。我们在有限矩和次Weibull条件下建立了最大范数的高斯近似结果，给出了维度可随网络规模增长的显式条件。我们还提出了一种高维网络HAC协方差估计器，并确立了其收敛性质，为同时推断提供了可行的方法。模拟研究表明，所提方法具有良好的有限样本性能。我们将该方法应用于研究溢出效应如何随网络同质性指数变化，通过为条件溢出效应函数构建置信带，应用结果揭示了传统低维推断会掩盖的异质性与局部显著性。
英文摘要
We develop a novel method of inference for network-dependent high-dimensional random vectors. Dependence is characterized via a functional dependence measure based on graph distance, allowing the approximation theory to capture the interaction between the decay of dependence and the growth of network neighborhoods. We establish Gaussian approximation results for the maximum norm under finite-moment and sub-Weibull conditions, providing explicit conditions under which the dimension may increase with the network size. We also propose a high-dimensional network HAC covariance estimator and establish its convergence properties, yielding a feasible procedure for simultaneous inference. Simulation studies demonstrate favorable finite-sample performance of the proposed method. We apply the procedure to study how spillover effects vary with an index of network homophily by constructing confidence bands for the conditional spillover-effect function. The application reveals heterogeneity and local significance that would be obscured by conventional low-dimensional inference.
