| 讲座简介： | We propose a novel network-varying coefficient model that extends traditional varying coefficient models to accommodate network data. The key idea is to model the regression coefficients as functions of the latent “locations” of network nodes that drive the formation of the network. To estimate the model, we identify the latent “locations” via the latent space model and develop an iterative projected gradient descent algorithm by optimizing the network parameters and regression coefficients alternately. The non-asymptotic bounds of the estimated coefficient matrix are obtained theoretically. Practically, the dimension of the latent space is chosen via a Bayesian information criterion. We further combine our method with a penalization procedure to select covariates with varying coefficients that are significant to the response variable and derive the related theoretical properties. The utility of the model is further illustrated via simulation studies as well as a real-world application in the field of finance by analyzing the relationship between stock returns and firm characteristics from a network perspective. The results show that the proposed model outperforms most existing methods. |
