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2018 Optimal prediction for additive function-on-function regression
Matthew Reimherr, Bharath Sriperumbudur, Bahaeddine Taoufik
Electron. J. Statist. 12(2): 4571-4601 (2018). DOI: 10.1214/18-EJS1505


As with classic statistics, functional regression models are invaluable in the analysis of functional data. While there are now extensive tools with accompanying theory available for linear models, there is still a great deal of work to be done concerning nonlinear models for functional data. In this work we consider the Additive Function-on-Function Regression model, a type of nonlinear model that uses an additive relationship between the functional outcome and functional covariate. We present an estimation methodology built upon Reproducing Kernel Hilbert Spaces, and establish optimal rates of convergence for our estimates in terms of prediction error. We also discuss computational challenges that arise with such complex models, developing a representer theorem for our estimate as well as a more practical and computationally efficient approximation. Simulations and an application to Cumulative Intraday Returns around the 2008 financial crisis are also provided.


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Matthew Reimherr. Bharath Sriperumbudur. Bahaeddine Taoufik. "Optimal prediction for additive function-on-function regression." Electron. J. Statist. 12 (2) 4571 - 4601, 2018.


Received: 1 September 2017; Published: 2018
First available in Project Euclid: 21 December 2018

zbMATH: 07003251
MathSciNet: MR3893421
Digital Object Identifier: 10.1214/18-EJS1505

Primary: 62G08 , 62G20

Keywords: Functional data analysis , minimax convergence , Nonlinear regression , ‎reproducing kernel Hilbert ‎space


Vol.12 • No. 2 • 2018
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