Outlier robust model selection in linear regression

Samuel Müller*, A. H. Welsh

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

48 Citations (Scopus)

Abstract

We propose a new approach to the selection of regression models based on combining a robust penalized criterion and a robust conditional expected prediction loss function that is estimated using a stratified bootstrap. Both components of the procedure use robust criteria (i.e., robust p-functions) rather than squared error loss to reduce the effects of large residuals and poor bootstrap samples. A key idea is to separate estimation from model selection by choosing estimators separately from the p-function. Using the stratified bootstrap further reduces the likelihood of obtaining poor bootstrap samples. We show that the model selection procedure is consistent under some conditions and works well in our simulations. In particular, we find that simultaneous minimization of prediction error and conditional expected prediction loss is better than separate minimization of the prediction error or the conditional expected prediction loss.

Original languageEnglish
Pages (from-to)1297-1310
Number of pages14
JournalJournal of the American Statistical Association
Volume100
Issue number472
DOIs
Publication statusPublished - Dec 2005
Externally publishedYes

Keywords

  • Bootstrap model selection
  • Outlier
  • Robust model selection
  • Schwarz bayesian information criterion
  • Stratified bootstrap

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