Smoothing Splines Estimators in Functional Linear Regression with Errors-in-Variables - Alois Kneip; Christophe Crambes; Herve Cardot; Pascal Sarda (University of Bonn, Bonn Graduate School of Economics (BGSE), 2006)
This work deals with a generalization of the Total Least Squares method in the context of the functional linear model. We first propose a smoothing splines estimator of the functional coefficient of the model without noise in the covariates and we obtain an asymptotic result for this estimator. Then, we adapt this estimator to the case where the covariates are noisy and we also derive an upper bound for the convergence speed. Our estimation procedure is evaluated by means of simulations.
Keywords: 330; Functional Linear Model; Smoothing Splines; Penalization; Errors-in-Variables; Total Least Squares