Network Cluster‐Robust Inference
研究了网络数据中聚类稳健推断方法的前提条件，证明聚类需具有低电导率，并利用谱图理论确定聚类数量与构造方法，对网络数据分析者选择推断方法有指导意义。
Since network data commonly consists of observations from a single large network, researchers often partition the network into clusters in order to apply cluster‐robust inference methods. Existing such methods require clusters to be asymptotically independent. Under mild conditions, we prove that, for this requirement to hold for network‐dependent data, it is necessary and sufficient that clusters have low conductance, the ratio of edge boundary size to volume. This yields a simple measure of cluster quality. We find in simulations that when clusters have low conductance, cluster‐robust methods control size better than HAC estimators. However, for important classes of networks lacking low‐conductance clusters, the former can exhibit substantial size distortion. To determine the number of low‐conductance clusters and construct them, we draw on results in spectral graph theory that connect conductance to the spectrum of the graph Laplacian. Based on these results, we propose to use the spectrum to determine the number of low‐conductance clusters and spectral clustering to construct them.