Penalized Nonparametric Scalar-on-Function Regression via Principal Coordinates. Issue 3 (3rd July 2017)

• Record Type: Journal Article
• Authors: Reiss, Philip T.; Miller, David L.; Wu, Pei-Shien; Hua, Wen-Yu
• Is Part Of: Journal of computational and graphical statistics. Volume 26:Issue 3(2017)
• Page Start: 569
• Page End: 578
• Publication Date: 2017-07-03
• Subjects: Dynamic time warping -- Functional regression -- Generalized additive model -- Kernel ridge regression -- Multidimensional scaling; Mathematical statistics -- Data processing -- Periodicals; Mathematical statistics -- Graphic methods -- Periodicals; 519.50285
• DOI: 10.1080/10618600.2016.1217227
• Languages: English
• ISSNs: 1061-8600

Abstract

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.