JSM 2011 Online Program

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Abstract Details

Activity Number: 273
Type: Invited
Date/Time: Tuesday, August 2, 2011 : 8:30 AM to 10:20 AM
Sponsor: Section on Nonparametric Statistics
Abstract - #300056
Title: Nonlinear Functional Regression
Author(s): Gareth James*+
Companies: University of Southern California
Address: IOM Department, Los Angeles, CA, 90089-0809,
Keywords: Functional Regression ; Nonlinear ; Penalized Regression
Abstract:

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 different functional predictors. Second, FAR extends beyond the standard linear regression setting to fit general non-linear 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 a real data set that FAR can significantly outperform competing methods.

This is joint work with Yingying Fan.


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