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On function-on-function regression: partial least squares approach

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Abstract

Functional data analysis tools, such as function-on-function regression models, have received considerable attention in various scientific fields because of their observed high-dimensional and complex data structures. Several statistical procedures, including least squares, maximum likelihood, and maximum penalized likelihood, have been proposed to estimate such function-on-function regression models. However, these estimation techniques produce unstable estimates in the case of degenerate functional data or are computationally intensive. To overcome these issues, we proposed a partial least squares approach to estimate the model parameters in the function-on-function regression model. In the proposed method, the B-spline basis functions are utilized to convert discretely observed data into their functional forms. Generalized cross-validation is used to control the degrees of roughness. The finite-sample performance of the proposed method was evaluated using several Monte-Carlo simulations and an empirical data analysis. The results reveal that the proposed method competes favorably with existing estimation techniques and some other available function-on-function regression models, with significantly shorter computational time.

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Acknowledgements

The authors acknowledge R code assistance from Dr. Fabian Scheipl at the Ludwig-Maximilians University of Munich and Ms. Julia Wrobel at Columbia University. The authors thank two anonymous referees for their careful reading of our manuscript and valuable suggestions and comments, which have helped us produce a much-improved paper. The second author also acknowledges the financial support from a research grant at the College of Business and Economics at the Australian National University.

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Authors and Affiliations

  1. Department of Statistics, Bartin University, Bartin, Turkey

    Ufuk Beyaztas

  2. Research School of Finance, Actuarial Studies, and Statistics, Australian National University, Level 4, Building 26C, Kingsley Street, Acton, ACT, 2601, Australia

    Han Lin Shang

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  1. Ufuk Beyaztas
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Correspondence to Han Lin Shang.

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Handling Editor: Bryan F. J. Manly

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Beyaztas, U., Shang, H.L. On function-on-function regression: partial least squares approach. Environ Ecol Stat 27, 95–114 (2020). https://doi.org/10.1007/s10651-019-00436-1

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