Abstract
Functional linear regression is at the centre of research attention involving curves as units of observation. In this article, we consider distributed computation in fitting functional linear regression with functional responses. We show that the aggregated estimator by simple averaging has the same convergence rate as the estimator using the entire data. Some simulation results are reported for illustration.
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Acknowledgements
The authors would like to thank the Editor-in-Chief, Professor Maria Kateri, an Associate Editor, and a reviewer for their insightful comments that have lead to significant improvement of the paper. The research of Jiamin Liu was supported by Fundamental Research Funds for the Central Universities (No. FRF-TP-22-105A1). The research of Heng Lian is supported by NSF Jiangxi Province (No. 20223BCJ25017), and by Hong Kong RGC general research fund 11300519, 11300721 and 11311822. The research of Rui Li was supported by National Social Science Foundation of China (No.17BTJ025).
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Liu, J., Li, R. & Lian, H. Distributed estimation of functional linear regression with functional responses. Metrika 87, 21–30 (2024). https://doi.org/10.1007/s00184-023-00902-8
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DOI: https://doi.org/10.1007/s00184-023-00902-8