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ABSTRACT
In this note, we consider the situation where we have a functional predictor as well as some more traditional scalar predictors, which we call the partially functional problem. We propose a semiparametric model based on sufficient dimension reduction, and thus our main interest is in dimension reduction although prediction can be carried out at a second stage. We establish root-n consistency of the linear part of the estimator. Some Monte Carlo studies are carried out as proof of concept.
2010 MATHEMATICS SUBJECT CLASSIFICATION:
Acknowledgments
The authors sincerely think the Editor, the Associate Editor and three reviewers for their insightful comments that significantly improved the paper.
Disclosure statement
No potential conflict of interest was reported by the authors.
Additional information
Funding
Yang's research was supported by the National Natural Science Foundation of China grants 11471086 and 11871173, National Social Science Foundation of China grant 16BTJ032, National Statistical Scientific Research Center Projects 2015LD02, and Fundamental Research Funds for the Central University 19JNYH08. Lin's research was partially supported by NSFC (11701360 and 11571112). Lian's research is supported by Hong Kong RGC General Research Fund 11301718 and NSFC No. 11871411.