TY - JOUR
T1 - Outlier robust model selection in linear regression
AU - Müller, Samuel
AU - Welsh, A. H.
PY - 2005/12
Y1 - 2005/12
N2 - 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.
AB - 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.
KW - Bootstrap model selection
KW - Outlier
KW - Robust model selection
KW - Schwarz bayesian information criterion
KW - Stratified bootstrap
UR - http://www.scopus.com/inward/record.url?scp=29144504107&partnerID=8YFLogxK
U2 - 10.1198/016214505000000529
DO - 10.1198/016214505000000529
M3 - Article
SN - 0162-1459
VL - 100
SP - 1297
EP - 1310
JO - Journal of the American Statistical Association
JF - Journal of the American Statistical Association
IS - 472
ER -