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2018 P-splines with an $\ell_{1}$ penalty for repeated measures
Brian D. Segal, Michael R. Elliott, Thomas Braun, Hui Jiang
Electron. J. Statist. 12(2): 3554-3600 (2018). DOI: 10.1214/18-EJS1487

Abstract

P-splines are penalized B-splines, in which finite order differences in coefficients are typically penalized with an $\ell_{2}$ norm. P-splines can be used for semiparametric regression and can include random effects to account for within-subject correlations. In addition to $\ell_{2}$ penalties, $\ell_{1}$-type penalties have been used in nonparametric and semiparametric regression to achieve greater flexibility, such as in locally adaptive regression splines, $\ell_{1}$ trend filtering, and the fused lasso additive model. However, there has been less focus on using $\ell_{1}$ penalties in P-splines, particularly for estimating conditional means.

In this paper, we demonstrate the potential benefits of using an $\ell_{1}$ penalty in P-splines with an emphasis on fitting non-smooth functions. We propose an estimation procedure using the alternating direction method of multipliers and cross validation, and provide degrees of freedom and approximate confidence bands based on a ridge approximation to the $\ell_{1}$ penalized fit. We also demonstrate potential uses through simulations and an application to electrodermal activity data collected as part of a stress study.

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Brian D. Segal. Michael R. Elliott. Thomas Braun. Hui Jiang. "P-splines with an $\ell_{1}$ penalty for repeated measures." Electron. J. Statist. 12 (2) 3554 - 3600, 2018. https://doi.org/10.1214/18-EJS1487

Information

Received: 1 July 2017; Published: 2018
First available in Project Euclid: 31 October 2018

zbMATH: 06970012
MathSciNet: MR3870506
Digital Object Identifier: 10.1214/18-EJS1487

Subjects:
Primary: 62G08
Secondary: 62P10

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Vol.12 • No. 2 • 2018
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