Journal
ELECTRONIC JOURNAL OF STATISTICS
Volume 12, Issue 2, Pages 4571-4601Publisher
INST MATHEMATICAL STATISTICS
DOI: 10.1214/18-EJS1505
Keywords
Nonlinear regression; functional data analysis; reproducing kernel Hilbert space; minimax convergence
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Funding
- NSF [DMS 1713011, DMS 1712826]
- NIDA [P50 DA039838]
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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.
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