Manuel Oviedo de la Fuente (Coruña University and MODES group of CITIC (Research Center for Information and Communication Technology))
Abstract :: The first part of this talk is a review of functional regression models with scalar response. These proposals are based on the extension of the ideas of generalized (linear or additive) models, GLM or GAM respectively for multivariate data to functional data covariates. One of our nonlinear models is based on constructing a Generalized Spectral Additive Model (FGSAM). The other one extends the kernel estimator (FGKAM), and it can be applied to general metric spaces since it is only based on distances. These algorithms would be applied to predict a binary response example (and extended to solve multiclass classification problems). The second part considers the problem of variable selection in regression models in the case of functional variables that may be mixed with other type of variables (scalar, multivariate, directional, etc.). This proposal begins with a simple null model and sequentially selects a new variable to be incorporated into the model based on the use of distance correlation. Finally, we propose three new approaches for additive functional regression models with functional responses. The first one is a reformulation of the linear regression model, and the last two are on the yet scarce case of additive functional regression models. Both proposals are based on extensions of similar models for scalar responses (FGSAM and FGKAM). All proporasals have shown quite promising results when applied to simulations and real data sets and have include in an R package fda.usc.