Abstract

We propose a novel functional linear model incorporating latent factors, where scalar

response, scalar covariates, and functional covariates have repeated measurements for each

subject. Our model accounts for latent factors that may impact the response but remain unobservable. To unveil and estimate these latent factors, we propose an iterated profile estimation

method. We then establish the consistency and asymptotic properties of the estimators. To

demonstrate the efficacy of our proposed estimation procedure, we conduct simulation studies

across various scenarios. We compare our results with estimations derived from conventional

functional linear models, revealing the superior performance of our method in addressing latent

factors. We further illustrate our proposed model and methodology by analyzing real data from

both financial markets and air pollution datasets. In these analyses, we successfully uncover

hidden factors that exert influence in these specific fields.

Information

Preprint No.SS-2024-0028
Manuscript IDSS-2024-0028
Complete AuthorsZixuan Han, Tao Li, Jinhong You, Jiguo Cao
Corresponding AuthorsJiguo Cao
EmailsJiguo_cao@sfu.ca

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Acknowledgments

The authors would like to thank the editor, the associate editor, and two referees for many insightful comments. These comments are very helpful for us

to improve our work. T. Li’s research was supported by the Humanities and

Social Science Fund of Ministry of Education of China (21YJA910001). J.

You’s research was supported by the National Natural Science Foundation

of China (Grant No.11971291) and Innovative Research Team of Shanghai

University of Finance and Economics. J. Cao’s research is supported by a

Discovery grant ( RGPIN-2023-04057) from the Natural Sciences and Engineering Research Council of Canada (NSERC) and the Canada Research

Chairs Program.

Supplementary Materials

The supplementary document includes the additional numerical results and

detailed proofs for theoretical results. We also provide the R codes for the

simulation studies and real data analysis on the website

Supplementary materials are available for download.