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

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  • Jialiang Li
  • Chao Huang
  • Zhub Hongtu

Abstract

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.

Suggested Citation

  • Jialiang Li & Chao Huang & Zhub Hongtu, 2017. "A Functional Varying-Coefficient Single-Index Model for Functional Response Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(519), pages 1169-1181, July.
    • Handle: RePEc:taf:jnlasa:v:112:y:2017:i:519:p:1169-1181
    DOI: 10.1080/01621459.2016.1195742
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    Cited by:

    1. Chen, Feifei & Jiang, Qing & Feng, Zhenghui & Zhu, Lixing, 2020. "Model checks for functional linear regression models based on projected empirical processes," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    2. Weicheng Zhu & Sheng Xu & Catherine C. Liu & Yehua Li, 2023. "Minimax powerful functional analysis of covariance tests with application to longitudinal genome‐wide association studies," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 50(1), pages 266-295, March.
    3. Zhensheng Huang & Xing Sun & Riquan Zhang, 2022. "Estimation for partially varying-coefficient single-index models with distorted measurement errors," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 85(2), pages 175-201, February.
    4. Rituparna Sen & Anandamayee Majumdar & Shubhangi Sikaria, 2022. "Bayesian Testing of Granger Causality in Functional Time Series," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 20(1), pages 191-210, September.
    5. Tao Huang & Jialiang Li, 2018. "Semiparametric model average prediction in panel data analysis," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 30(1), pages 125-144, January.
    6. Qian Huang & Jinhong You & Liwen Zhang, 2022. "Efficient inference of longitudinal/functional data models with time‐varying additive structure," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(2), pages 744-771, June.
    7. Minhee Kim & Todd Allen & Kaibo Liu, 2023. "Covariate Dependent Sparse Functional Data Analysis," INFORMS Joural on Data Science, INFORMS, vol. 2(1), pages 81-98, April.
    8. Zhu, Hanbing & Zhang, Yuanyuan & Li, Yehua & Lian, Heng, 2023. "Semiparametric function-on-function quantile regression model with dynamic single-index interactions," Computational Statistics & Data Analysis, Elsevier, vol. 182(C).
    9. Xiong Cai & Liugen Xue & Xiaolong Pu & Xingyu Yan, 2021. "Efficient Estimation for Varying-Coefficient Mixed Effects Models with Functional Response Data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(4), pages 467-495, May.
    10. Ruiyan Luo & Xin Qi, 2023. "Nonlinear function‐on‐scalar regression via functional universal approximation," Biometrics, The International Biometric Society, vol. 79(4), pages 3319-3331, December.
    11. Xue, Liugen & Zhang, Jinghua, 2020. "Empirical likelihood for partially linear single-index models with missing observations," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    12. Yunlong Nie & Liangliang Wang & Jiguo Cao, 2023. "Estimating functional single index models with compact support," Environmetrics, John Wiley & Sons, Ltd., vol. 34(2), March.

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