A Functional Varying-Coefficient Single-Index Model for Functional Response Data

• 成果类型: Article
• 署名作者: Li, Jialiang; Huang, Chao; Zhu, Hongtu
• 署名单位: National University of Singapore; University of North Carolina; University of North Carolina Chapel Hill; University of Texas System; UTMD Anderson Cancer Center
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2016.1195742
• 发表日期: 2017
• 页码: 1169-1181
• 关键词: Longitudinal Data; Dimension Reduction; linear-models; regression

摘要

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.