Li Jialiang, Huang Chao, Zhu Hongtu
Associate Professor in Department of Statistics and Applied Probability in National University of Singapore, an Associate Professor in Duke-NUS Graduate Medical School and a Scientist in Singapore Eye Research Institute.
A doctoral student under the supervision of Dr. Hongtu Zhu.
J Am Stat Assoc. 2017;112(519):1169-1181. doi: 10.1080/01621459.2016.1195742. Epub 2017 Apr 25.
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.
受成像数据分析的启发，我们提出了一种新颖的功能变系数单指标模型（FVCSIM），用于对一组感兴趣的协变量进行功能响应数据的回归分析。FVCSIM是从横断面和纵向研究中收集的标量响应的变系数单指标模型的新扩展。我们开发了一种有效的估计程序，以迭代方式估计变系数函数、链接函数、指标参数向量以及各个函数的协方差函数。我们系统地研究了所有估计量的渐近性质，包括估计的变系数函数的弱收敛性、估计的指标参数向量的渐近分布以及估计的协方差函数及其谱的一致收敛速度。进行了模拟研究以评估所提出程序的有限样本性能。我们应用FVCSIM来研究从阿尔茨海默病神经影像倡议（ADNI）研究中获得的沿胼胝体骨架的白质扩散率的发展情况。
