Time‐varying β‐model for dynamic directed networks
将经典β模型扩展到动态有向网络，用核平滑似然方法估计随时间变化的参数，并证明估计量的一致性及渐近正态性，适用于分析随时间变化的网络数据。
Abstract We extend the well‐known ‐model for directed graphs to dynamic network setting, where we observe snapshots of adjacency matrices at different time points. We propose a kernel‐smoothed likelihood approach for estimating time‐varying parameters in a network with nodes, from snapshots. We establish consistency and asymptotic normality properties of our kernel‐smoothed estimators as either or diverges. Our results contrast their counterparts in single‐network analyses, where is invariantly required in asymptotic studies. We conduct comprehensive simulation studies that confirm our theory's prediction and illustrate the performance of our method from various angles. We apply our method to an email dataset and obtain meaningful results.