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June 2022 A robust partial least squares approach for function-on-function regression
Ufuk Beyaztas, Han Lin Shang
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Braz. J. Probab. Stat. 36(2): 199-219 (June 2022). DOI: 10.1214/21-BJPS523


The function-on-function linear regression model in which the response and predictors consist of random curves has become a general framework to investigate the relationship between the functional response and functional predictors. Existing methods to estimate the model parameters may be sensitive to outlying observations, common in empirical applications. In addition, these methods may be severely affected by such observations, leading to undesirable estimation and prediction results. A robust estimation method, based on iteratively reweighted simple partial least squares, is introduced to improve the prediction accuracy of the function-on-function linear regression model in the presence of outliers. The performance of the proposed method is based on the number of partial least squares components used to estimate the function-on-function linear regression model. Thus, the optimum number of components is determined via a data-driven error criterion. The finite-sample performance of the proposed method is investigated via several Monte Carlo experiments and an empirical data analysis. In addition, a nonparametric bootstrap method is applied to construct pointwise prediction intervals for the response function. The results are compared with some of the existing methods to illustrate the improvement potentially gained by the proposed method.

Funding Statement

This work was supported by The Scientific and Technological Research Council of Turkey (TUBITAK) (grant no: 120F270).


We thank Editor-in-chief, AE, and two reviewers for their constructive comments, which have helped us produce a much-improved paper. We thank Dr. Aylin Alin for providing some R code.


Download Citation

Ufuk Beyaztas. Han Lin Shang. "A robust partial least squares approach for function-on-function regression." Braz. J. Probab. Stat. 36 (2) 199 - 219, June 2022.


Received: 1 May 2021; Accepted: 1 November 2021; Published: June 2022
First available in Project Euclid: 5 May 2022

Digital Object Identifier: 10.1214/21-BJPS523

Keywords: basis function , Dimension reduction , SIMPLS , weighted likelihood

Rights: Copyright © 2022 Brazilian Statistical Association


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Vol.36 • No. 2 • June 2022
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