Smoothing splines estimators in functional linear regression with errors-in-variables

Authors:
Hervé Cardot;Christophe Crambes;Alois Kneip;Pascal Sarda
Affiliations:
INRA Dijon, CESAER - ENESAD, 26, bd Docteur Petitjean, BP 87999, 21079 Dijon Cedex, France;Laboratoire de Statistique et Probabilités, Université Paul Sabatier, UMR C5583, 118, route de Narbonne, 31062 Toulouse Cedex, France;Statistische Abteilung, Department of Economics, Universität Bonn, Adenauerallee 24, 53113 Bonn, Germany;Laboratoire de Statistique et Probabilités, Université Paul Sabatier, UMR C5583, 118, route de Narbonne, 31062 Toulouse Cedex, France
Venue:
Computational Statistics & Data Analysis
Year:
2007

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Abstract

The total least squares method is generalized in the context of the functional linear model. A smoothing splines estimator of the functional coefficient of the model is first proposed without noise in the covariates and an asymptotic result for this estimator is obtained. Then, this estimator is adapted to the case where the covariates are noisy and an upper bound for the convergence speed is also derived. The estimation procedure is evaluated by means of simulations.