Additive prediction and boosting for functional data

Additive model and estimates for regression problems involving functional data are proposed. The impact of the additive methodology for analyzing datasets involving various functional covariates is underlined by comparing its predictive power with those of standard (i.e. non additive) nonparametric functional regression methods. The comparison is made both from a theoretical point of view, and from a real environmental functional dataset. As a by-product, the method is also used for boosting nonparametric functional data analysis even in situations where a single functional covariate is observed. A second functional dataset, coming from spectrometric analysis, illustrates the interest of this functional boosting procedure.