TY - JOUR
T1 - A Functional Varying-Coefficient Single-Index Model for Functional Response Data
AU - for the Alzheimer's Disease Neuroimaging Initiative
AU - Li, Jialiang
AU - Huang, Chao
AU - Hongtu, Zhub
N1 - Publisher Copyright:
© 2017 American Statistical Association.
PY - 2017/7/3
Y1 - 2017/7/3
N2 - Motivated by the analysis of imaging data, we propose a novel functional varying-coefficient single-index model (FVCSIM) to carry out the regression analysis of functional response data on a set of covariates of interest. FVCSIM represents a new extension of varying-coefficient single-index models for scalar responses collected from cross-sectional and longitudinal studies. An efficient estimation procedure is developed to iteratively estimate varying coefficient functions, link functions, index parameter vectors, and the covariance function of individual functions. We systematically examine the asymptotic properties of all estimators including the weak convergence of the estimated varying coefficient functions, the asymptotic distribution of the estimated index parameter vectors, and the uniform convergence rate of the estimated covariance function and their spectrum. Simulation studies are carried out to assess the finite-sample performance of the proposed procedure. We apply FVCSIM to investigate the development of white matter diffusivities along the corpus callosum skeleton obtained from Alzheimer’s Disease Neuroimaging Initiative (ADNI) study. Supplementary material for this article is available online.
AB - Motivated by the analysis of imaging data, we propose a novel functional varying-coefficient single-index model (FVCSIM) to carry out the regression analysis of functional response data on a set of covariates of interest. FVCSIM represents a new extension of varying-coefficient single-index models for scalar responses collected from cross-sectional and longitudinal studies. An efficient estimation procedure is developed to iteratively estimate varying coefficient functions, link functions, index parameter vectors, and the covariance function of individual functions. We systematically examine the asymptotic properties of all estimators including the weak convergence of the estimated varying coefficient functions, the asymptotic distribution of the estimated index parameter vectors, and the uniform convergence rate of the estimated covariance function and their spectrum. Simulation studies are carried out to assess the finite-sample performance of the proposed procedure. We apply FVCSIM to investigate the development of white matter diffusivities along the corpus callosum skeleton obtained from Alzheimer’s Disease Neuroimaging Initiative (ADNI) study. Supplementary material for this article is available online.
KW - Functional data analysis
KW - Image data analysis
KW - Single-index model
KW - Varying-coefficient model
UR - http://www.scopus.com/inward/record.url?scp=85018717031&partnerID=8YFLogxK
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U2 - 10.1080/01621459.2016.1195742
DO - 10.1080/01621459.2016.1195742
M3 - Article
C2 - 29200540
AN - SCOPUS:85018717031
SN - 0162-1459
VL - 112
SP - 1169
EP - 1181
JO - Journal of the American Statistical Association
JF - Journal of the American Statistical Association
IS - 519
ER -