The Annals of Statistics
- Ann. Statist.
- Volume 43, Number 5 (2015), 2296-2325.
Functional additive regression
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.
Ann. Statist., Volume 43, Number 5 (2015), 2296-2325.
Received: November 2014
Revised: May 2015
First available in Project Euclid: 16 September 2015
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Fan, Yingying; James, Gareth M.; Radchenko, Peter. Functional additive regression. Ann. Statist. 43 (2015), no. 5, 2296--2325. doi:10.1214/15-AOS1346. https://projecteuclid.org/euclid.aos/1442364153
- Supplementary material for: Functional additive regression. Due to space constraints, the proofs of Theorems 1 and 2 and Lemma 1 are relegated to the supplement .