Functional Linear Regression with Functional Response

Benatia, David, Carrasco, Marine and Florens, Jean-Pierre (2017) Functional Linear Regression with Functional Response. Journal of Econometrics, 201 (2). pp. 269-291.

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Official URL: http://tse-fr.eu/pub/32454

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.

Item Type: Article
Language: English
Date: 2017
Refereed: Yes
Uncontrolled Keywords: Functional regression, Instrumental variables, Linear operator, Tikhonov regularization
Subjects: B- ECONOMIE ET FINANCE
Divisions: TSE-R (Toulouse)
Site: UT1
Date Deposited: 13 Apr 2018 14:39
Last Modified: 13 Apr 2018 14:39
OAI ID: oai:tse-fr.eu:32454
URI: http://publications.ut-capitole.fr/id/eprint/25840

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