Partially linear model selection by the bootstrap

Samuel Müller*, Céline Vial

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


Summary We propose a new approach to the selection of partially linear models based on the conditional expected prediction square loss function, which is estimated using the bootstrap. Because of the different speeds of convergence of the linear and the nonlinear parts, a key idea is to select each part separately. In the first step, we select the nonlinear components using an 'm-out-of-n' residual bootstrap that ensures good properties for the nonparametric bootstrap estimator. The second step selects the linear components from the remaining explanatory variables, and the non-zero parameters are selected based on a two-level residual bootstrap. We show that the model selection procedure is consistent under some conditions, and our simulations suggest that it selects the true model most often than the other selection procedures considered.

Original languageEnglish
Pages (from-to)183-200
Number of pages18
JournalAustralian and New Zealand Journal of Statistics
Issue number2
Publication statusPublished - Jun 2009
Externally publishedYes


  • consistent model selection
  • partially linear model
  • residual bootstrap model selection


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