Component selection in the additive regression model

Xia Cui, Heng Peng*, Songqiao Wen, Lixing Zhu

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

12 Citations (Scopus)
22 Downloads (Pure)


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.

Original languageEnglish
Pages (from-to)491-510
Number of pages20
JournalScandinavian Journal of Statistics
Issue number3
Publication statusPublished - Sept 2013

Scopus Subject Areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

User-Defined Keywords

  • Additive model
  • Generalized cross-validation
  • Group variable selection
  • Lasso
  • Non-parametric component
  • Penalized splines


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