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Distributed estimation of functional linear regression with functional responses

Author

Listed:
  • Jiamin Liu

    (University of Science and Technology Beijing)

  • Rui Li

    (Shanghai University of International Business and Economics)

  • Heng Lian

    (CityU Shenzhen Research Institute
    City University of Hong Kong)

Abstract

Functional linear regression is at the centre of research attention involving curves as units of observation. In this article, we consider distributed computation in fitting functional linear regression with functional responses. We show that the aggregated estimator by simple averaging has the same convergence rate as the estimator using the entire data. Some simulation results are reported for illustration.

Suggested Citation

  • Jiamin Liu & Rui Li & Heng Lian, 2024. "Distributed estimation of functional linear regression with functional responses," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 87(1), pages 21-30, January.
    • Handle: RePEc:spr:metrik:v:87:y:2024:i:1:d:10.1007_s00184-023-00902-8
    DOI: 10.1007/s00184-023-00902-8
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    References listed on IDEAS

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    1. Benatia, David & Carrasco, Marine & Florens, Jean-Pierre, 2017. "Functional linear regression with functional response," Journal of Econometrics, Elsevier, vol. 201(2), pages 269-291.
    2. Ariel Kleiner & Ameet Talwalkar & Purnamrita Sarkar & Michael I. Jordan, 2014. "A scalable bootstrap for massive data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 76(4), pages 795-816, September.
    3. Frédéric Ferraty & Philippe Vieu, 2002. "The Functional Nonparametric Model and Application to Spectrometric Data," Computational Statistics, Springer, vol. 17(4), pages 545-564, December.
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