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Single-index Varying Coefficient Model for Functional Responses

Institution:
1School of Finance and Statistics, East China Normal University, Shanghai, China.
2Department of Biostatistics and Biomedical Research Imaging Center, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina, USA.
3Department of Mathematics, Hong Kong Baptist University, Hong Kong, China.
Publisher:
Wiley
Publication Date:
Dec-2016
Journal:
Biometrics
Volume Number:
72
Issue Number:
4
Pages:
1275-84
Citation:
Biometrics. 2016 Dec;72(4):1275-84.
PubMed ID:
27061414
PMCID:
PMC5055851
Keywords:
Functional response, Image analysis, Single index, Uniform convergence, Varying coefficient
Appears in Collections:
NA-MIC
Sponsors:
UL1 TR001111/TR/NCATS NIH HHS/United States
U54 EB005149/EB/NIBIB NIH HHS/United States
R01 MH086633/MH/NIMH NIH HHS/United States
T32 MH106440/MH/NIMH NIH HHS/United States
R21 AG033387/AG/NIA NIH HHS/United States
R01 EB020426/EB/NIBIB NIH HHS/United States
Generated Citation:
Luo X., Zhu L., Zhu H. Single-index Varying Coefficient Model for Functional Responses. Biometrics. 2016 Dec;72(4):1275-84. PMID: 27061414. PMCID: PMC5055851.
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Recently, massive functional data have been widely collected over space across a set of grid points in various imaging studies. It is interesting to correlate functional data with various clinical variables, such as age and gender, in order to address scientific questions of interest. The aim of this article is to develop a single-index varying coefficient (SIVC) model for establishing a varying association between functional responses (e.g., image) and a set of covariates. It enjoys several unique features of both varying-coefficient and single-index models. An estimation procedure is developed to estimate varying coefficient functions, the index function, and the covariance function of individual functions. The optimal integration of information across different grid points is systematically delineated and the asymptotic properties (e.g., consistency and convergence rate) of all estimators are examined. Simulation studies are conducted to assess the finite-sample performance of the proposed estimation procedure. Furthermore, our real data analysis of a white matter tract dataset obtained from the Alzheimer's Disease Neuroimaging Initiative (ADNI) study confirms the advantage and accuracy of SIVC model over the popular varying coefficient model.