RT Generic
T1 Penalized function-on-function partial leastsquares regression
A1 Hernandez Roig, Harold Antonio
A1 Aguilera Morillo, María del Carmen
A1 Aguilera, Ana M.
A1 Preda, Cristian
A2 Universidad Carlos III de Madrid. Departamento de Estadística, 
AB 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.
SN 2387-0303
YR 2023
FD 2023-07-05
LK https://hdl.handle.net/10016/37758
UL https://hdl.handle.net/10016/37758
LA eng
DS e-Archivo
RD 17 jun. 2024