title: Single-index varying coefficient model for functional responses.
abstract: 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.
authors.affiliation: School of Finance and Statistics, East China Normal University, Shanghai, China.|Department of Biostatistics and Biomedical Research Imaging Center, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina, U.S.A.
authors.forename: Xinchao
authors.initials: X
authors.lastname: Luo
authors.affiliation: Department of Mathematics, Hong Kong Baptist University, Hong Kong, China.
authors.forename: Lixing
authors.initials: L
authors.lastname: Zhu
authors.affiliation: Department of Biostatistics and Biomedical Research Imaging Center, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina, U.S.A.
authors.forename: Hongtu
authors.initials: H
authors.lastname: Zhu
mesh_terms: D000544:Alzheimer Disease / Q000000981:diagnostic imaging*; D003198:Computer Simulation; D006801:Humans; D015233:Models, Statistical; D059906:Neuroimaging / Q000706:statistics & numerical data*; D066127:White Matter / Q000000981:diagnostic imaging
keywords: Functional response; Image analysis; Single index; Uniform convergence; Varying coefficient