On the robustness of the adaptive lasso to model misspecification

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 generaliz...

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Bibliographic Details
Published in:Biometrika 2012-09, Vol.99 (3), p.717-731
Main Authors: LU, W., GOLDBERG, Y., FINE, J. P.
Format: Article
Language:English
Subjects:
Applications
Asymptotic methods
Biology, psychology, social sciences
Censorship
Consistent estimators
Diabetic retinopathy
Estimating techniques
Estimators
Exact sciences and technology
General topics
Generalized linear model
Generalized linear models
Mathematical models
Mathematics
Modeling
Nonparametric inference
Oracles
Parameter estimation
Parametric inference
Parametric models
Probability and statistics
Regression analysis
Regression coefficients
Sciences and techniques of general use
Statistics
Studies
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Summary: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.
ISSN:0006-3444
1464-3510
DOI:10.1093/biomet/ass027