We propose a nonparametric \(\beta \) -model for modelling the evolution of node degrees in dynamic networks. The model has n unknown parameter functions; therefore, a statistical analysis is challenging. We develop an adaptive weighted approach for estimating n parameter functions considering the network similarity between nearby time points. The proposed estimator performs well, even when the coefficient functions are piecewise smooth. We establish the consistency and asymptotic normality of the proposed estimator, which has smaller variance than the point-wise maximum likelihood estimator. In dynamic network data, it is also important to detect time points where the behavior of some nodes exhibits a sudden change in structure. We further develop inference methods for the change-point detection problem based on the proposed estimator. It dramatically improves statistical power by pooling information from nearby time points and can precisely identify the locations of change-points with a probability tending toward one. We evaluate the finite sample performance of the proposed method using extensive simulation studies and illustrate its application using an ant social organization dataset.
