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Functional linear regression with functional response

David Benatia, Marine Carrasco and Jean-Pierre Florens

Journal of Econometrics, 2017, vol. 201, issue 2, 269-291

Abstract: In this paper, we develop new estimation results for functional regressions where both the regressor Z(t) and the response Y(t) are functions of Hilbert spaces, indexed by the time or a spatial location. The model can be thought as a generalization of the multivariate regression where the regression coefficient is now an unknown operator Π. We propose to estimate the operator Π by Tikhonov regularization, which amounts to apply a penalty on the L2 norm of Π. We derive the rate of convergence of the mean-square error, the asymptotic distribution of the estimator, and develop tests on Π. As trajectories are often not fully observed, we consider the scenario where the data become more and more frequent (infill asymptotics). We also address the case where Z is endogenous and instrumental variables are used to estimate Π. An application to the electricity consumption completes the paper.

Keywords: Functional regression; Instrumental variables; Linear operator; Tikhonov regularization (search for similar items in EconPapers)
JEL-codes: C13 (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1016/j.jeconom.2017.08.008

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Journal of Econometrics is currently edited by T. Amemiya, A. R. Gallant, J. F. Geweke, C. Hsiao and P. M. Robinson

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