Penalized nonparametric scalar-on-function regression via principal coordinates
Abstract
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.
Citation
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 . https://doi.org/10.1080/10618600.2016.1217227
Publication
Journal of Computational and Graphical Statistics
Status
Peer reviewed
ISSN
1061-8600Type
Journal article
Description
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).Collections
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