A new scalar-on-function generalized additive model for partially observed functional data: an application to image classification.

Pavel Hernández-Amaro, Universidad Carlos III de Madrid

Co-authors: Maria Durban, Universidad Carlos III; Maria del Carmen Aguilera Morillo, Universitat Politecnica de Valencia

Abstract: In this work we present a novel methodology to fit a generalized additive functional regression model for partially observed functional data. This approach avoids the functional reconstruction and assumes the basis representation of both, the functional coefficient and the functional covariate. The model’s coefficients are estimated via Penalized Quasi-likelihood using the mixed model representation of a penalized spline. The performance of the proposed model is tested via two simulation studies, one for uni-dimensional functional data and another for two-dimensional functional data. Finally, the methodology is used to classify air pollution collected from a real dataset of images in a region of India.