The Annals of Statistics

Functional additive regression

Yingying Fan, Gareth M. James, and Peter Radchenko

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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.

Article information

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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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

Functional regression shrinkage single index model variable selection


Fan, Yingying; James, Gareth M.; Radchenko, Peter. Functional additive regression. Ann. Statist. 43 (2015), no. 5, 2296--2325. doi:10.1214/15-AOS1346.

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Supplemental materials

  • 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 [12].