Functional Linear Model with Prior Information of Subjects' Network

In many modern applications, data samples are interconnected by a network, and network information is a crucial factor in forecasting. However, existing network data analysis methods, which are designed for scalar data, are not effective for infinite-dimensional function data, particularly when functional predictors are observed on an irregular sampling design. In this article, we propose a functional linear model for network-linked data. To improve the estimation and prediction, the network cohesion is enforced using the Laplace quadratic penalty function. The statistical properties of the proposed model are studied, and an extension to high-dimensional functional data is developed to simultaneously select relevant functional predictors and estimate the coefficient functions. Simulation results and real data application demonstrate the satisfactory performance of the proposed methods. Supplementary materials for this article are available online.