Electronic Journal of Statistics

Optimal prediction for additive function-on-function regression

Matthew Reimherr, Bharath Sriperumbudur, and Bahaeddine Taoufik

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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.

Article information

Electron. J. Statist., Volume 12, Number 2 (2018), 4571-4601.

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

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Mathematical Reviews number (MathSciNet)

Primary: 62G08: Nonparametric regression 62G20: Asymptotic properties

Nonlinear regression functional data analysis reproducing kernel Hilbert space minimax convergence

Creative Commons Attribution 4.0 International License.


Reimherr, Matthew; Sriperumbudur, Bharath; Taoufik, Bahaeddine. Optimal prediction for additive function-on-function regression. Electron. J. Statist. 12 (2018), no. 2, 4571--4601. doi:10.1214/18-EJS1505. https://projecteuclid.org/euclid.ejs/1545382950

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