Penalized Nonparametric Scalar-on-Function Regression via Principal Coordinates |
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Authors: | Philip T Reiss David L Miller Pei-Shien Wu Wen-Yu Hua |
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Institution: | 1. Department of Child and Adolescent Psychiatry and Department of Population Health, New York University, New York, NY, and Department of Statistics, University of Haifa, Haifa, Israelreiss@stat.haifa.ac.il;3. Integrated Statistics, Woods Hole, MA, and Centre for Research into Ecological and Environmental Modelling and School of Mathematics and Statistics, University of St Andrews, St Andrews, United Kingdom;4. Department of Child and Adolescent Psychiatry, New York University, New York, NY |
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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. |
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Keywords: | Dynamic time warping Functional regression Generalized additive model Kernel ridge regression Multidimensional scaling |
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