Penalized nonparametric scalar-on-function regression via principal coordinates
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A number of classical approaches to nonparametric regression have recently been extended to the case of functional predictors. This article introduces a new method of this type, which extends intermediate-rank penalized smoothing to scalar-on-function regression. In the proposed method, which we call principal coordinate ridge regression, one regresses the response on leading principal coordinates defined by a relevant distance among the functional predictors, while applying a ridge penalty. Our publicly available implementation, based on generalized additive modeling software, allows for fast optimal tuning parameter selection and for extensions to multiple functional predictors, exponential family-valued responses, and mixed-effects models. In an application to signature verification data, principal coordinate ridge regression, with dynamic time warping distance used to define the principal coordinates, is shown to outperform a functional generalized linear model. Supplementary materials for this article are available online.
Reiss , P T , Miller , D L , Wu , P S & Hua , W Y 2017 , ' Penalized nonparametric scalar-on-function regression via principal coordinates ' Journal of Computational and Graphical Statistics , vol 26 , no. 3 , pp. 569-587 . DOI: 10.1080/10618600.2016.1217227
Journal of Computational and Graphical Statistics
© 2017, American Statistical Association, Institute of Mathematical Statistics, and Interface Foundation of North America. This work has been made available online in accordance with the publisher’s policies. This is the author created, accepted version manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at www.tandfonline.com / http://dx.doi.org/10.1080/10618600.2016.1217227
Philip Reiss, Pei-Shien Wu, and Wen-Yu Hua gratefully acknowledge the support of the U.S. National Institute of Mental Health (grant 1R01MH095836-01A1).
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