Functional additive regression Article Swipe
YOU?
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· 2015
· Open Access
·
· DOI: https://doi.org/10.1214/15-aos1346
· OA: W1942126059
We suggest a new method, called Functional Additive Regression, or FAR, for\nefficiently performing high-dimensional functional regression. FAR extends the\nusual linear regression model involving a functional predictor, $X(t)$, and a\nscalar response, $Y$, in two key respects. First, FAR uses a penalized least\nsquares optimization approach to efficiently deal with high-dimensional\nproblems involving a large number of functional predictors. Second, FAR extends\nbeyond the standard linear regression setting to fit general nonlinear additive\nmodels. We demonstrate that FAR can be implemented with a wide range of penalty\nfunctions using a highly efficient coordinate descent algorithm. Theoretical\nresults are developed which provide motivation for the FAR optimization\ncriterion. Finally, we show through simulations and two real data sets that FAR\ncan significantly outperform competing methods.\n
