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Abstract Details
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Activity Number:
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452
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Type:
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Topic Contributed
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Date/Time:
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Wednesday, August 3, 2011 : 8:30 AM to 10:20 AM
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Sponsor:
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Biometrics Section
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| Abstract - #301891 |
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Title:
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Functional Additive Regression
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Author(s):
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Yingying Fan*+ and Gareth James
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Companies:
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University of Southern California and University of Southern California
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Address:
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Hoffman Hall, Los Angeles, CA, 90089, USA
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Keywords:
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Variable Selection ;
Functional Regression ;
Additive Model ;
Single Index Model ;
Shrinkage
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Abstract:
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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 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.
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