Single-index varying coefficient model for functional responses

Xinchao Luo, Lixing ZHU, Hongtu Zhu*

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

16 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)1275-1284
Number of pages10
Issue number4
Publication statusPublished - 1 Dec 2016

Scopus Subject Areas

  • Statistics and Probability
  • Biochemistry, Genetics and Molecular Biology(all)
  • Immunology and Microbiology(all)
  • Agricultural and Biological Sciences(all)
  • Applied Mathematics

User-Defined Keywords

  • Functional response
  • Image analysis
  • Single index
  • Uniform convergence
  • Varying coefficient


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