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Multivariate functional linear regression and prediction

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  • Chiou, Jeng-Min
  • Yang, Ya-Fang
  • Chen, Yu-Ting

Abstract

We propose a multivariate functional linear regression (mFLR) approach to analysis and prediction of multivariate functional data in cases in which both the response and predictor variables contain multivariate random functions. The mFLR model, coupled with the multivariate functional principal component analysis approach, takes the advantage of cross-correlation between component functions within the multivariate response and predictor variables, respectively. The estimate of the matrix of bivariate regression functions is consistent in the sense of the multi-dimensional Gram–Schmidt norm and is asymptotically normally distributed. The prediction intervals of the multivariate random trajectories are available for predictive inference. We show the finite sample performance of mFLR by a simulation study and illustrate the method through predicting multivariate traffic flow trajectories for up-to-date and partially observed traffic streams.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:146:y:2016:i:c:p:301-312
    DOI: 10.1016/j.jmva.2015.10.003
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    7. Łukasz Smaga & Hidetoshi Matsui, 2018. "A note on variable selection in functional regression via random subspace method," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 27(3), pages 455-477, August.
    8. Cody Carroll & Hans‐Georg Müller & Alois Kneip, 2021. "Cross‐component registration for multivariate functional data, with application to growth curves," Biometrics, The International Biometric Society, vol. 77(3), pages 839-851, September.
    9. Shuzhi Zhu & Peixin Zhao, 2019. "Tests for the linear hypothesis in semi-functional partial linear regression models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 82(2), pages 125-148, March.
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    11. Jiang, Jiakun & Lin, Huazhen & Zhong, Qingzhi & Li, Yi, 2022. "Analysis of multivariate non-gaussian functional data: A semiparametric latent process approach," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    12. Ufuk Beyaztas & Han Lin Shang, 2021. "A partial least squares approach for function-on-function interaction regression," Computational Statistics, Springer, vol. 36(2), pages 911-939, June.
    13. Yang, Yang & Yang, Yanrong & Shang, Han Lin, 2022. "Feature extraction for functional time series: Theory and application to NIR spectroscopy data," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    14. Ajroldi, Niccolò & Diquigiovanni, Jacopo & Fontana, Matteo & Vantini, Simone, 2023. "Conformal prediction bands for two-dimensional functional time series," Computational Statistics & Data Analysis, Elsevier, vol. 187(C).
    15. Cody Carroll & Hans‐Georg Müller, 2023. "Latent deformation models for multivariate functional data and time‐warping separability," Biometrics, The International Biometric Society, vol. 79(4), pages 3345-3358, December.
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    18. Vieu, Philippe, 2018. "On dimension reduction models for functional data," Statistics & Probability Letters, Elsevier, vol. 136(C), pages 134-138.

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