Time‐varying β‐model for dynamic directed networks

Abstract

AbstractWe 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.