Statistica Sinica 22 (2012), 69-94

doi:http://dx.doi.org/10.5705/ss.2010.085

PRESMOOTHING IN FUNCTIONAL

LINEAR REGRESSION

Frédéric Ferraty$^1$, Wenceslao González-Manteiga$^2$,

Adela Martínez-Calvo$^2$ and Philippe Vieu$^1$

$^1$Université Paul Sabatier and $^2$Universidade de Santiago de Compostela

Abstract: In this paper, we consider the functional linear model with scalar response, and explanatory variable valued in a function space. In recent literature, functional principal components analysis (FPCA) has been used to estimate the model parameter. We propose to modify this approach by using presmoothing techniques. For this new estimate, consistency is stated and efficiency by comparison with the standard FPCA estimator is studied. We have also analysed the behaviour of our presmoothed estimator by means of a simulation study and data applications.

Key words and phrases: Functional linear regression (FLR), functional principal components analysis (FPCA), nonparametric kernel estimator, presmoothing.