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.
Bibliographical notePublisher Copyright:
© 2017 American Statistical Association, Institute of Mathematical Statistics, and Interface Foundation of North America.
- Dynamic time warping
- Functional regression
- Generalized additive model
- Kernel ridge regression
- Multidimensional scaling
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics
- Statistics and Probability
- Statistics, Probability and Uncertainty