On the robustness of the adaptive lasso to model misspecification

• 成果类型: Article
• 署名作者: Lu, W.; Goldberg, Y.; Fine, J. P.
• 署名单位: North Carolina State University; University of North Carolina; University of North Carolina Chapel Hill
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/ass027
• 发表日期: 2012
• 页码: 717731
• 关键词: nonconcave penalized likelihood; variable selection; diverging number; diabetic-retinopathy; inference; progression

摘要

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.