Functional Linear Model with Prior Information of Subjects’ Network
针对网络关联的函数型数据，提出一种函数线性模型，利用拉普拉斯二次惩罚函数增强网络内聚性，并扩展至高维情形以同时选择预测变量和估计系数函数。
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.