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

Authors:
Pang Du;Guang Cheng;Hua Liang
Affiliations:
Department of Statistics, Virginia Tech, Blacksburg, VA, United States;Department of Statistics, Purdue University, West Lafayette, IN, United States;Department of Biostatistics and Computational Biology, University of Rochester, Rochester, NY 14642, United States
Venue:
Computational Statistics & Data Analysis
Year:
2012

Citing 1
Cited 1

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Abstract

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 L"2-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.