TY - JOUR
T1 - Component selection in the additive regression model
AU - Cui, Xia
AU - Peng, Heng
AU - Wen, Songqiao
AU - Zhu, Lixing
N1 - Funding information:
Xia Cui's research is supported by a grant from National Nature Science Foundation of China (NNSF, 11101442) and a specialized Research Fund for the Doctoral Program of Higher Education of China (SRFDP 20100171120042). Heng Peng's research is supported by CERG grants of Hong Kong Research Grant Council (HKBU 201809, HKBU 201610 and HKBU 202012), FRG grants from Hong Kong Baptist University (FRG/08-09/II-33, FRG/10-11/024 and FRG/11-12/130) and a grant from National Nature Science Foundation of China (NNSF 11271094). Songqiao Wen's research was supported by a grant from National Natural Science Foundation of China (NNSF 10901109). Lixing Zhu was supported by a CERG grant of Hong Kong Research Grant Council, Hong Kong.
Peng and Zhu are in charge of the methodology development and material organization. The authors thank the editor, associate editor and referees for their constructive suggestions which led to a significant improvement of an early manuscript.
Publisher copyright:
© 2013 Board of the Foundation of the Scandinavian Journal of Statistics. Published by Wiley Publishing Ltd.
PY - 2013/9
Y1 - 2013/9
N2 - Similar to variable selection in the linear model, selecting significant components in the additive model is of great interest. However, such components are unknown, unobservable functions of independent variables. Some approximation is needed. We suggest a combination of penalized regression spline approximation and group variable selection, called the group-bridge-type spline method (GBSM), to handle this component selection problem with a diverging number of correlated variables in each group. The proposed method can select significant components and estimate non-parametric additive function components simultaneously. To make the GBSM stable in computation and adaptive to the level of smoothness of the component functions, weighted power spline bases and projected weighted power spline bases are proposed. Their performance is examined by simulation studies. The proposed method is extended to a partial linear regression model analysis with real data, and gives reliable results.
AB - Similar to variable selection in the linear model, selecting significant components in the additive model is of great interest. However, such components are unknown, unobservable functions of independent variables. Some approximation is needed. We suggest a combination of penalized regression spline approximation and group variable selection, called the group-bridge-type spline method (GBSM), to handle this component selection problem with a diverging number of correlated variables in each group. The proposed method can select significant components and estimate non-parametric additive function components simultaneously. To make the GBSM stable in computation and adaptive to the level of smoothness of the component functions, weighted power spline bases and projected weighted power spline bases are proposed. Their performance is examined by simulation studies. The proposed method is extended to a partial linear regression model analysis with real data, and gives reliable results.
KW - Additive model
KW - Generalized cross-validation
KW - Group variable selection
KW - Lasso
KW - Non-parametric component
KW - Penalized splines
UR - http://www.scopus.com/inward/record.url?scp=84881559214&partnerID=8YFLogxK
U2 - 10.1111/j.1467-9469.2012.00823.x
DO - 10.1111/j.1467-9469.2012.00823.x
M3 - Journal article
AN - SCOPUS:84881559214
SN - 0303-6898
VL - 40
SP - 491
EP - 510
JO - Scandinavian Journal of Statistics
JF - Scandinavian Journal of Statistics
IS - 3
ER -