Semiparametric regression models with additive nonparametric components and high dimensional parametric components

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• 作者：Pang Du^a ; ^{pangdu@vt.edu} ; Guang Cheng^b ; ^{chengg@purdue.edu} ; Hua Liang^c ; ^{hliang@bst.rochester.edu}
• 关键词：Additive models ; Backfitting ; Model selection ; Partial smoothing splines ; SCAD ; Sparsity
• 刊名：Computational Statistics and Data Analysis
• 出版年：2012
• 期刊代码：19_01679473
• 类别：cp
• 出版时间：June, 2012
• 卷：56
• 期：6
• 页码：2006-2017
• 文件大小：320 K

摘要

This paper concerns semiparametric regression models with additive nonparametric components and high dimensional parametric components under sparsity assumptions. To achieve simultaneous model selection for both nonparametric and parametric parts, we introduce a penalty that combines the adaptive empirical -norms of the nonparametric component functions and the SCAD penalty on the coefficients in the parametric part. We use the additive partial smoothing spline estimate as the initial estimate and establish its convergence rate with diverging dimensions of parametric components. Our simulation studies reveal excellent model selection performance of the proposed method. An application to an economic study on Canadian household gasoline consumption reveals interesting results.