title: On the robustness of the adaptive lasso to model misspecification.
abstract: 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.
authors.affiliation: Department of Statistics, North Carolina State University, 2311 Stinson Drive, 5212 SAS Hall, Raleigh, North Carolina 27695-8203, U.S.A., lu@stat.ncsu.edu.
authors.forename: W
authors.initials: W
authors.lastname: Lu
authors.affiliation: Department of Biostatistics, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599-7420, U.S.A., yair.goldy@gmail.com , jfine@email.unc.edu.
authors.forename: Y
authors.initials: Y
authors.lastname: Goldberg
authors.affiliation: Department of Biostatistics, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599-7420, U.S.A., yair.goldy@gmail.com , jfine@email.unc.edu.
authors.forename: J P
authors.initials: JP
authors.lastname: Fine
keywords: Least false parameter; Model misspecification; Oracle property; Penalization; Selection consistency; Shrinkage estimation; Variable selection