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Variable selection in varying coefficient models using P-splines

Abstract : In this article, we consider nonparametric smoothing and variable selection in varying-coefficient models. Varying-coefficient models are commonly used for analyzing the time-dependent effects of covariates on responses measured repeatedly (such as longitudinal data). We present the P-spline estimator in this context and show its estimation consistency for a diverging number of knots (or B-spline basis functions). The combination of P-splines with nonnegative garrote (which is a variable selection method) leads to good estimation and variable selection. Moreover, we consider APSO (additive P-spline selection operator), which combines a P-spline penalty with a regularization penalty, and show its estimation and variable selection consistency. The methods are illustrated with a simulation study and real-data examples. The proofs of the theoretical results as well as one of the real-data examples are provided in the online supplementary materials.
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https://hal.inria.fr/hal-00851197
Contributor : Brigitte Bidégaray-Fesquet <>
Submitted on : Monday, August 12, 2013 - 11:37:41 PM
Last modification on : Thursday, November 19, 2020 - 1:01:09 PM

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Anestis Antoniadis, Irène Gijbels, Anneleen Verhasselt. Variable selection in varying coefficient models using P-splines. Journal of Computational and Graphical Statistics, Taylor & Francis, 2012, 21 (3), pp.638-661. ⟨10.1080/10618600.2012.680826⟩. ⟨hal-00851197⟩

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