Two-way Homogeneity Pursuit for Quantile Network Vector Autoregression

Motivated by prior studies on network effects in directed networks, our model assigns each node two latent group memberships to flexibly capture asymmetric and heterogeneous interactions among users. These memberships, along with model parameters, can be consistently estimated using the proposed estimation procedure.

As a result, the model performs node clustering and parameter estimation simultaneously, striking a balance between model flexibility and interpretability. We establish theoretical guarantees for the proposed method, showing that both group memberships and parameter estimators are consistent even when the number of groups is over-specified. When the group numbers are correctly specified, the parameter estimators are asymptotically normal, enabling valid statistical inference.