Penalization methods have been shown to yield both consistent variable selection and oracle parameter estimation under correct model specification. In this article, we study such methods under model misspecification, where the assumed form of the regression function is incorrect, including generalized linear models for uncensored outcomes and the proportional hazards model for censored responses. Estimation with the adaptive least absolute shrinkage and selection operator, lasso, penalty is proven to achieve sparse estimation of regression coefficients under misspecification. The resulting estimators are selection consistent, asymptotically normal and oracle, where the selection is based on the limiting values of the parameter estimators obtained using the misspecified model without penalization. We further derive conditions under which the penalized estimators from the misspecified model may yield selection consistency under the true model. The robustness is explored numerically via simulation and an application to the Wisconsin Epidemiological Study of Diabetic Retinopathy.
Bibliographical noteFunding Information:
We would like to thank Michael Kosorok for helpful discussions regarding misspecification of frailty models. We also thank the editor, an associate editor and three referees for very insightful comments. Lu and Fine’s research was supported by the National Cancer Institute.
- Least false parameter
- Model misspecification
- Oracle property
- Selection consistency
- Shrinkage estimation
- Variable selection
ASJC Scopus subject areas
- Statistics and Probability
- Mathematics (all)
- Agricultural and Biological Sciences (miscellaneous)
- Agricultural and Biological Sciences (all)
- Statistics, Probability and Uncertainty
- Applied Mathematics