PARTIALLY LINEAR ADDITIVE FUNCTIONAL REGRESSION

Xiaohui Liu; Wenqi Lu; Heng Lian; Yuzi Liu; Zhongyi Zhu

doi:10.5705/ss.202020.0418

PARTIALLY LINEAR ADDITIVE FUNCTIONAL REGRESSION

Xiaohui Liu, Wenqi Lu, Heng Lian^*, Yuzi Liu, Zhongyi Zhu

^*Corresponding author for this work

Department of Mathematics

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

2 Citations (Scopus)

127 Downloads (CityUHK Scholars)

Abstract

We consider a novel partially linear additive functional regression model in which both a functional predictor and some scalar predictors appear. The functional part has a semiparametric continuously additive form, while the scalar predictors appear in the linear part. The functional part has the optimal convergence rate, and the asymptotic normality of the nonfunctional part is also shown. Simulations and an empirical analysis of a Covid-19 data set demonstrate the performance of the proposed estimator.

Original language	English
Pages (from-to)	2199-2216
Journal	Statistica Sinica
Volume	32
Issue number	4
DOIs	https://doi.org/10.5705/ss.202020.0418
Publication status	Published - Oct 2022

Funding

"We sincerely thank the editor Prof. Yuan-chin Chang, Prof. Rong Chen, an associate editor, and two anonymous reviewers for their insightful comments. The research of Heng Lian was supported by Project 11871411 from the NSFC and the Shenzhen Research Institute, City University of Hong Kong, and by Hong Kong RGC general research fund 11301718, 11300519, and 11300721. The research of Xiaohui Liu was supported by the NNSF of China (Grant No.11971208, 11601197), China Postdoctoral Science Foundation funded project (2016M600511, 2017T100475), and NSF of Jiangxi Province (No. 2018ACB21002, 20171ACB21 030, 20192BAB201005)."

Research Keywords

Convergence rate
functional data
penalization
RKHS
EFFICIENT ESTIMATION
MODELS
CONVERGENCE
SELECTION
SINGLE

Publisher's Copyright Statement

COPYRIGHT TERMS OF DEPOSITED FINAL PUBLISHED VERSION FILE: Statistica Sinica © 2022 Institute of Statistical Science, Academia Sinica. Use of this article is permitted solely for educational and research purposes. Liu, X., Lu, W., Lian, H., Liu, Y., & Zhu, Z. (2022). PARTIALLY LINEAR ADDITIVE FUNCTIONAL REGRESSION. Statistica Sinica, 32(4), 2199-2216. https://doi.org/10.5705/ss.202020.0418.

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title = "PARTIALLY LINEAR ADDITIVE FUNCTIONAL REGRESSION",

abstract = "We consider a novel partially linear additive functional regression model in which both a functional predictor and some scalar predictors appear. The functional part has a semiparametric continuously additive form, while the scalar predictors appear in the linear part. The functional part has the optimal convergence rate, and the asymptotic normality of the nonfunctional part is also shown. Simulations and an empirical analysis of a Covid-19 data set demonstrate the performance of the proposed estimator.",

keywords = "Convergence rate, functional data, penalization, RKHS, EFFICIENT ESTIMATION, MODELS, CONVERGENCE, SELECTION, SINGLE",

author = "Xiaohui Liu and Wenqi Lu and Heng Lian and Yuzi Liu and Zhongyi Zhu",

year = "2022",

month = oct,

doi = "10.5705/ss.202020.0418",

language = "English",

volume = "32",

pages = "2199--2216",

journal = "Statistica Sinica",

issn = "1017-0405",

publisher = "Academia Sinica * Institute of Statistical Science",

number = "4",

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TY - JOUR

T1 - PARTIALLY LINEAR ADDITIVE FUNCTIONAL REGRESSION

AU - Liu, Xiaohui

AU - Lu, Wenqi

AU - Lian, Heng

AU - Liu, Yuzi

AU - Zhu, Zhongyi

PY - 2022/10

Y1 - 2022/10

N2 - We consider a novel partially linear additive functional regression model in which both a functional predictor and some scalar predictors appear. The functional part has a semiparametric continuously additive form, while the scalar predictors appear in the linear part. The functional part has the optimal convergence rate, and the asymptotic normality of the nonfunctional part is also shown. Simulations and an empirical analysis of a Covid-19 data set demonstrate the performance of the proposed estimator.

AB - We consider a novel partially linear additive functional regression model in which both a functional predictor and some scalar predictors appear. The functional part has a semiparametric continuously additive form, while the scalar predictors appear in the linear part. The functional part has the optimal convergence rate, and the asymptotic normality of the nonfunctional part is also shown. Simulations and an empirical analysis of a Covid-19 data set demonstrate the performance of the proposed estimator.

KW - Convergence rate

KW - functional data

KW - penalization

KW - RKHS

KW - EFFICIENT ESTIMATION

KW - MODELS

KW - CONVERGENCE

KW - SELECTION

KW - SINGLE

UR - http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=LinksAMR&SrcApp=PARTNER_APP&DestLinkType=FullRecord&DestApp=WOS&KeyUT=000862824800020

U2 - 10.5705/ss.202020.0418

DO - 10.5705/ss.202020.0418

M3 - RGC 21 - Publication in refereed journal

SN - 1017-0405

VL - 32

SP - 2199

EP - 2216

JO - Statistica Sinica

JF - Statistica Sinica

IS - 4

ER -

PARTIALLY LINEAR ADDITIVE FUNCTIONAL REGRESSION

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Research Keywords

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GRF: Distributed Estimation with Random Projection in Reproducing Kernel Hilbert Spaces

GRF: Low-rank tensor as a Dimension Reduction Tool in Complex Data Analysis

GRF: Divide and Conquer in High-dimensional Statistical Models

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PARTIALLY LINEAR ADDITIVE FUNCTIONAL REGRESSION

Abstract

Funding

Research Keywords

Publisher's Copyright Statement

Access Output

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Permanent Link

Other Files and Links

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Projects

GRF: Distributed Estimation with Random Projection in Reproducing Kernel Hilbert Spaces

GRF: Low-rank tensor as a Dimension Reduction Tool in Complex Data Analysis

GRF: Divide and Conquer in High-dimensional Statistical Models

Cite this