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, prediction methods are devised that are similar to minimum average variance estimation (MAVE) or functional sliced inverse regression (FSIR). Their practical implementation is described, together with their application both to simulated and on real data analyzing three calibration examples of near infrared spectra.