Problem
Research questions and friction points this paper is trying to address.
High-Dimensional Network Data
Inference
Graph Distance
Network Dependence
Gaussian Approximation
Inference for High-Dimensional Network Data
🤖 AI Summary
本文提出了一种新的方法，用于处理网络依赖的高维随机向量，通过基于图距离的功能依赖度量来刻画依赖关系，并开发了高维网络HAC协方差估计器以进行同时推断。
📝 Abstract
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.
Innovation
Methods, ideas, or system contributions that make the work stand out.
functional dependence measure
high-dimensional network HAC covariance estimator
Gaussian approximation
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