Penalized Spline Estimation for Varying-Coefficient Models |
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Authors: | Yiqiang Lu Riquan Zhang Liping Zhu |
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Affiliation: | 1. Institute of Electronic Technology , The PLA Information Engineering University , Zhengzhou, P.R. China yiqiang_lu@163.com;3. Department of Statistics , East China Normal University , Shanghai, P.R. China |
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Abstract: | Varying-coefficient models are useful extensions of classical linear models. They arise from multivariate nonparametric regression, nonlinear time series modeling and forecasting, longitudinal data analysis, and others. This article proposes the penalized spline estimation for the varying-coefficient models. Assuming a fixed but potentially large number of knots, the penalized spline estimators are shown to be strong consistency and asymptotic normality. A systematic optimization algorithm for the selection of multiple smoothing parameters is developed. One of the advantages of the penalized spline estimation is that it can accommodate varying degrees of smoothness among coefficient functions due to multiple smoothing parameters being used. Some simulation studies are presented to illustrate the proposed methods. |
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Keywords: | Generalized cross validation (GCV) Penalized spline Smoothing parameter estimation Varying-coefficient models |
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