Dimension reduction in functional regression with applications

Two dimensional reduction regression methods to predict a scalar response from a discretized sample path of a continuous time covariate process are presented. The methods take into account the functional nature of the predictor and are both based on appropriate wavelet decompositions. Using such decompositions, we derive prediction methods that are similar to minimum average variance estimation (MAVE) or functional sliced inverse regression (FSIR). We describe their practical implementation and we apply the method both in simulation and on real data analyzing three calibration examples of near infrared spectra.