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October 2015 Functional additive regression
Yingying Fan, Gareth M. James, Peter Radchenko
Ann. Statist. 43(5): 2296-2325 (October 2015). DOI: 10.1214/15-AOS1346


We suggest a new method, called Functional Additive Regression, or FAR, for efficiently performing high-dimensional functional regression. FAR extends the usual linear regression model involving a functional predictor, $X(t)$, and a scalar response, $Y$, in two key respects. First, FAR uses a penalized least squares optimization approach to efficiently deal with high-dimensional problems involving a large number of functional predictors. Second, FAR extends beyond the standard linear regression setting to fit general nonlinear additive models. We demonstrate that FAR can be implemented with a wide range of penalty functions using a highly efficient coordinate descent algorithm. Theoretical results are developed which provide motivation for the FAR optimization criterion. Finally, we show through simulations and two real data sets that FAR can significantly outperform competing methods.


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Yingying Fan. Gareth M. James. Peter Radchenko. "Functional additive regression." Ann. Statist. 43 (5) 2296 - 2325, October 2015.


Received: 1 November 2014; Revised: 1 May 2015; Published: October 2015
First available in Project Euclid: 16 September 2015

zbMATH: 1327.62252
MathSciNet: MR3396986
Digital Object Identifier: 10.1214/15-AOS1346

Primary: 62G08
Secondary: 62G20

Keywords: functional regression , shrinkage , Single index model , Variable selection

Rights: Copyright © 2015 Institute of Mathematical Statistics


Vol.43 • No. 5 • October 2015
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