A Functional Varying-Coefficient Single-Index Model for Functional Response Data
针对影像数据等函数型响应变量，提出变系数单指标模型，给出估计方法和渐近性质，并用于分析ADNI研究中白质弥散性沿胼胝体骨架的变化。
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 investigating the development of white matter diffusivities along the corpus callosum skeleton obtained from Alzheimer's Disease Neuroimaging Initiative (ADNI) study.