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.
Original language | English |
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Pages (from-to) | 569-578 |
Number of pages | 10 |
Journal | Journal of Computational and Graphical Statistics |
Volume | 26 |
Issue number | 3 |
DOIs | |
State | Published - 3 Jul 2017 |
Bibliographical note
Publisher Copyright:© 2017 American Statistical Association, Institute of Mathematical Statistics, and Interface Foundation of North America.
Keywords
- Dynamic time warping
- Functional regression
- Generalized additive model
- Kernel ridge regression
- Multidimensional scaling
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty
- Discrete Mathematics and Combinatorics