Functional linear regression with functional response

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...

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Bibliographic Details
Published in:Journal of econometrics 2017-12, Vol.201 (2), p.269-291
Main Authors: Benatia, David, Carrasco, Marine, Florens, Jean-Pierre
Format: Article
Language:English
Subjects:
Consumption
Convergence
Electricity
Endogenous
Estimating techniques
Functional regression
Humanities and Social Sciences
Infill
Instrumental variables
Linear operator
Mathematics
Quantitative Finance
Regression analysis
Spatial location
Statistics
Studies
Tikhonov regularization
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Summary: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.
ISSN:0304-4076
1872-6895
DOI:10.1016/j.jeconom.2017.08.008