Variable Selection in Varying-Coefficient Models Using P-Splines |
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Authors: | Anestis Antoniadis Irène Gijbels Anneleen Verhasselt |
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Institution: | 1. Laboratoire Jean Kuntzmann , Université Joseph Fourier , Grenoble , 38041 , France;2. Department of Mathematics and Leuven Statistics Research Center (LStat) , Katholieke Universiteit Leuven (KU Leuven) , 3001 , Heverlee , Belgium;3. Department of Mathematics and Computer Science , Universiteit Antwerpen , 2020 , Antwerpen , Belgium |
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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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Keywords: | Longitudinal data Nonparametric smoothing Penalized splines Selecting variables Varying regression coefficients |
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