Functional Linear Model with Prior Information of Subjects’ Network

Abstract

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.

KEYWORDS:

• Functional principal component analysis
• High-dimensional functional data
• Laplacian quadratic penalty

Supplementary Materials

Supplementary materials include a pdf file providing proofs, additional simulation results and application results, and code to replicate the simulated and real-world examples.

Acknowledgments

The authors are very grateful to the Editor, Associate Editor, and two reviewers for their constructive comments and insightful suggestions that substantially improve the original manuscript.

Disclosure Statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This study was supported by the National Natural Science Foundation of China (72071169, 11971404, 72233002), Humanity and Social Science Youth Foundation of Ministry of Education of China (19YJC910010, 20YJC910004), National Social Science Foundation of China (21&ZD 146), China Postdoctoral Science Foundation (2021M701999), Shandong Provincial Natural Science Foundation (ZR2022QA049), and the Fundamental Research Funds for the Central Universities of China (20720231060).