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

Ufuk Beyaztas, Han Lin Shang

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)


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.
Original languageEnglish
Pages (from-to)95–114
Number of pages20
JournalEnvironmental and Ecological Statistics
Issue number1
Publication statusPublished - 7 Mar 2020
Externally publishedYes


  • Basis function
  • Functional data
  • Nonparametric smoothing


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