Penalised functional partial least squares regression with multiple covariates

C. Díaz-Louzao, M. C. Aguilera-Morillo, A. J. Ferrer-Riquelme

The direct estimation of a function-on-function regression model is usually an ill-posed problem because both the functional variables and the coefficients have infinite dimension. In practice, the first step is to obtain the functional data by assuming an expansion of each sample curve in terms of basis functions and then to estimate the basis coefficients by smoothing techniques. In this context, we extend the penalised version of the function-on-function partial least squares approach to the multivariate case. This approach imposes smoothness on the PLS weights by introducing 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. Penalising the PLS weights imposes smoothness on the resulting coefficient function, improving its interpretability. To illustrate the benefits of our model, we applied it synthetic and real data sets.

Keywords: multivariate functional data, functional PLS, P-spline penalty

GT Análisis de Datos Funcionales I
September 4, 2026  9:00 AM
Aula 30

P. Galeano San Miguel

S. Novo Díaz, G. Aneiros Pérez

D. Diz Castro, M. Febrero Bande, W. González Manteiga

A. Elías Fernández