Abstract

We consider a large-scale network where a scalar response and a functional predictor are

observed for each individual. To incorporate the network information and to depict the dynamic impact

of the functional predictor on the response of each individual, we investigate a network functional linear

model. The model assumes that each individual’s response can be explained by a linear combination

of the responses of the neighbors and a functional regression of the individual. We first approximate

functional regression coefficient by a finite representation based on functional principal component

analysis technique (FPCA) and then introduce a novel least-squares type of procedure to estimate

the coefficients after dimension reduction. In addition, we introduce two modified BIC-type criteria

for choosing the number of principal components. We study the convergence rates of the functional

regression coefficients and establish the asymptotic normality of the network autoregression coefficients,

as well as the consistency of the model selection procedures. Extensive simulation studies are conducted

to evaluate the finite sample performance of our proposed method. Finally, we illustrate the usefulness

of our method by applying it to two applications.

Information

Preprint No.SS-2024-0282
Manuscript IDSS-2024-0282
Complete AuthorsXingyu Yan, Yanyuan Ma
Corresponding AuthorsXingyu Yan
Emailsyan@jsnu.edu.cn

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Acknowledgments

We are grateful to the Editor, an anonymous Associate Editor and reviewers for their careful

reading and valuable suggestions, which have helped to improve the article. This research

was supported by the National Key R&D Program of China under Grant 2024YFA1012200,

the National Natural Science Foundation of China under Grant 12571285, and the National

Institute of Health.

Supplementary Materials

The Supplementary Material contains auxiliary lemmas, additional simulation results, theoretical analysis, and all proofs of Theorems 1-4.

Supplementary materials are available for download.