report · e-Archivo (Carlos III University of Madrid) · 2023

Penalized function-on-function partial leastsquares regression

Hernandez Roig, Harold Antonio, Aguilera Morillo, María del Carmen, Aguilera, Ana M., Preda, Cristian

Cited by 0Open access

Abstract

This paper deals with the "function-on-function'" or "fully functional" linear regression problem. We address the problem by proposing a novel penalized Function-on-Function Partial Least-Squares (pFFPLS) approach that imposes smoothness on the PLS weights. Our proposal introduces an appropriate finite-dimensional functional space with an associated set of bases on which to represent the data and controls smoothness with a roughness penalty operator. Penalizing the PLS weights imposes smoothness on the resulting coefficient function, improving its interpretability. In a simulation study, we demonstrate the advantages of pFFPLS compared to non-penalized FFPLS. Our comparisons indicate a higher accuracy of pFFPLS when predicting the response and estimating the true coefficient function from which the data were generated. We also illustrate the advantages of our proposal with two case studies involving two well-known datasets from the functional data analysis literature. In the first one, we predict log precipitation curves from the yearly temperature profiles recorded in 35 weather stations in Canada. In the second case study, we predict the hip angle profiles during a gait cycle of children from their corresponding knee angle profiles.

Cite this paper

APA 7

Hernandez Roig, H. A., Aguilera Morillo, M. D. C., Aguilera, A. M., & Preda, C. (2023). Penalized function-on-function partial leastsquares regression. e-Archivo (Carlos III University of Madrid).

MLA 9

Hernandez Roig, Harold Antonio, et al. “Penalized function-on-function partial leastsquares regression.” e-Archivo (Carlos III University of Madrid), 2023.

Chicago

Hernandez Roig, Harold Antonio, María del Carmen Aguilera Morillo, Ana M. Aguilera, and Cristian Preda. 2023. “Penalized function-on-function partial leastsquares regression.” e-Archivo (Carlos III University of Madrid).

Harvard

Hernandez Roig, H.A. et al. (2023) ‘Penalized function-on-function partial leastsquares regression’, e-Archivo (Carlos III University of Madrid).

BibTeX

@article{hernandezroig2023penalized,
  title = {{Penalized function-on-function partial leastsquares regression}},
  author = {Hernandez Roig, Harold Antonio and Aguilera Morillo, María del Carmen and Aguilera, Ana M. and Preda, Cristian},
  journal = {e-Archivo (Carlos III University of Madrid)},
  year = {2023}
}

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