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Adaptive smoothing spline estimator for the function-on-function linear regression model

Author

Listed:
  • Fabio Centofanti

    (University of Naples Federico II)

  • Antonio Lepore

    (University of Naples Federico II)

  • Alessandra Menafoglio

    (MOX - Modelling and Scientific Computing, Department of Mathematics, Politecnico di Milano)

  • Biagio Palumbo

    (University of Naples Federico II)

  • Simone Vantini

    (MOX - Modelling and Scientific Computing, Department of Mathematics, Politecnico di Milano)

Abstract

In this paper, we propose an adaptive smoothing spline (AdaSS) estimator for the function-on-function linear regression model where each value of the response, at any domain point, depends on the full trajectory of the predictor. The AdaSS estimator is obtained by the optimization of an objective function with two spatially adaptive penalties, based on initial estimates of the partial derivatives of the regression coefficient function. This allows the proposed estimator to adapt more easily to the true coefficient function over regions of large curvature and not to be undersmoothed over the remaining part of the domain. A novel evolutionary algorithm is developed ad hoc to obtain the optimization tuning parameters. Extensive Monte Carlo simulations have been carried out to compare the AdaSS estimator with competitors that have already appeared in the literature before. The results show that our proposal mostly outperforms the competitor in terms of estimation and prediction accuracy. Lastly, those advantages are illustrated also in two real-data benchmark examples. The AdaSS estimator is implemented in the R package adass, openly available online on CRAN.

Suggested Citation

  • Fabio Centofanti & Antonio Lepore & Alessandra Menafoglio & Biagio Palumbo & Simone Vantini, 2023. "Adaptive smoothing spline estimator for the function-on-function linear regression model," Computational Statistics, Springer, vol. 38(1), pages 191-216, March.
    • Handle: RePEc:spr:compst:v:38:y:2023:i:1:d:10.1007_s00180-022-01223-6
    DOI: 10.1007/s00180-022-01223-6
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    References listed on IDEAS

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    More about this item

    Keywords

    Functional data analysis; Function-on-function linear regression; Adaptive smoothing; Functional regression;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C19 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Other

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