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Multivariate functional group sparse regression: Functional predictor selection

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  • Ali Mahzarnia
  • Jun Song
Abstract
In this paper, we propose methods for functional predictor selection and the estimation of smooth functional coefficients simultaneously in a scalar-on-function regression problem under a high-dimensional multivariate functional data setting. In particular, we develop two methods for functional group-sparse regression under a generic Hilbert space of infinite dimension. We show the convergence of algorithms and the consistency of the estimation and the selection (oracle property) under infinite-dimensional Hilbert spaces. Simulation studies show the effectiveness of the methods in both the selection and the estimation of functional coefficients. The applications to functional magnetic resonance imaging (fMRI) reveal the regions of the human brain related to ADHD and IQ.

Suggested Citation

  • Ali Mahzarnia & Jun Song, 2022. "Multivariate functional group sparse regression: Functional predictor selection," PLOS ONE, Public Library of Science, vol. 17(4), pages 1-22, April.
    • Handle: RePEc:plo:pone00:0265940
    DOI: 10.1371/journal.pone.0265940
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    References listed on IDEAS

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    2. Song, Jun & Li, Bing, 2021. "Nonlinear and additive principal component analysis for functional data," Journal of Multivariate Analysis, Elsevier, vol. 181(C).
    3. Yao, Fang & Muller, Hans-Georg & Wang, Jane-Ling, 2005. "Functional Data Analysis for Sparse Longitudinal Data," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 577-590, June.
    4. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
    5. Hui Zou & Trevor Hastie, 2005. "Addendum: Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(5), pages 768-768, November.
    6. Hui Zou & Trevor Hastie, 2005. "Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(2), pages 301-320, April.
    7. Chiou, Jeng-Min & Yang, Ya-Fang & Chen, Yu-Ting, 2016. "Multivariate functional linear regression and prediction," Journal of Multivariate Analysis, Elsevier, vol. 146(C), pages 301-312.
    8. Clara Happ & Sonja Greven, 2018. "Multivariate Functional Principal Component Analysis for Data Observed on Different (Dimensional) Domains," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(522), pages 649-659, April.
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