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Smoothing Splines Estimators in Functional Linear Regression with Errors-in-Variables

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  • Kneip, Alois
  • Crambes, Christophe
  • Cardot, Herve
  • Sarda, Pascal

Abstract

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.

Suggested Citation

  • Kneip, Alois & Crambes, Christophe & Cardot, Herve & Sarda, Pascal, 2006. "Smoothing Splines Estimators in Functional Linear Regression with Errors-in-Variables," Bonn Econ Discussion Papers 2/2006, University of Bonn, Bonn Graduate School of Economics (BGSE).
    • Handle: RePEc:zbw:bonedp:22006
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    References listed on IDEAS

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    1. Cardot, Hervé & Ferraty, Frédéric & Sarda, Pascal, 1999. "Functional linear model," Statistics & Probability Letters, Elsevier, vol. 45(1), pages 11-22, October.
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    Cited by:

    1. Comte , Fabienne & Johannes, Jan, 2011. "Adaptive functional linear regression," LIDAM Discussion Papers ISBA 2011038, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).

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