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Reduced rank modeling for functional regression with functional responses

Author

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  • Lin, Hongmei
  • Jiang, Xuejun
  • Lian, Heng
  • Zhang, Weiping

Abstract

This article considers regression problems where both the predictor and the response are functional in nature. Driven by the desire to build a parsimonious model, we consider functional reduced rank regression in the framework of reproducing kernel Hilbert spaces, which can be formulated in the form of linear factor regression with estimated multivariate factors, and achieves dimension reduction in both the predictor and the response spaces. The convergence rate of the estimator is derived. Simulations and real datasets are used to demonstrate the competitive performance of the proposed method.

Suggested Citation

  • Lin, Hongmei & Jiang, Xuejun & Lian, Heng & Zhang, Weiping, 2019. "Reduced rank modeling for functional regression with functional responses," Journal of Multivariate Analysis, Elsevier, vol. 169(C), pages 205-217.
    • Handle: RePEc:eee:jmvana:v:169:y:2019:i:c:p:205-217
    DOI: 10.1016/j.jmva.2018.09.004
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    References listed on IDEAS

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    6. Lian, Heng, 2015. "Minimax prediction for functional linear regression with functional responses in reproducing kernel Hilbert spaces," Journal of Multivariate Analysis, Elsevier, vol. 140(C), pages 395-402.
    7. Izenman, Alan Julian, 1975. "Reduced-rank regression for the multivariate linear model," Journal of Multivariate Analysis, Elsevier, vol. 5(2), pages 248-264, June.
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