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Summary: Dimension Reduction in Functional
Regression with Applications
U. Amato a
A. Antoniadis b
I. De Feis a
aIstituto per le Applicazioni del Calcolo `M. Picone' CNR - Sezione di Napoli, Via
Pietro Castellino 111, 80131 Napoli, Italy
bLaboratoire de Modelisation et Calcul (LMC-IMAG), Universite Joseph Fourier,
Tour IRMA, B.P. 53, 38041 Grenoble, CEDEX 9, France
Abstract
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 pre-
diction methods that are similar to minimum average variance estimation (MAVE)
or functional sliced inverse regression (FSIR). We describe their practical imple-
mentation and we apply the method both in simulation and on real data analyzing
three calibration examples of near infrared spectra.
Key words: dimension reduction; wavelets; MAVE; SIR
1 Introduction
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