Advances in functional regression and classification models

Abstract

Functional data analysis (FDA) has become a very active field of research in the last few years because it appears naturally in most scientific fields: energy (electricity price curves), environment (curves of pollutant levels), chemometrics (spectrometric data), etc. This thesis is a compendium of the following publications: 1) "Statistical computing in functional data analysis: the R package fda.usc" published in the J STAT SOFTW, the core advances of this paper was to propose a common framework for FDA in R. 2) "Predicting seasonal influenza transmission using functional regression models with temporal dependence" published in PLoS ONE proposes an extension of GLS model to functional case. 3) "The DD$^G$--classifier in the functional setting" published in TEST extends the DD-classifier using information derived of the functional depth. 4) "Determining optimum wavelengths for leaf water content estimation from reflectance: A distance correlation approach" published in CHEMOMETR INTELL LAB SYST studies the utility of distance correlation as a method to select impact points in functional regression. 5) "Variable selection in Functional Additive Regression Models", in Comput Stat proposes a variable selection algorithm in the case of mixed predictors (scalar, functional, etc.).