Bridge estimators and the adaptive Lasso under heteroscedasticity
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Date
2011-07-04
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Abstract
In this paper we investigate penalized least squares methods in linear regression models
with heteroscedastic error structure. It is demonstrated that the basic properties with respect to model selection and parameter estimation of bridge estimators, Lasso and adaptive Lasso do not change if the assumption of homoscedasticity is violated. However, these estimators do not have oracle properties in the sense of Fan and Li (2001). In order to address this problem we introduce weighted penalized least squares methods and demonstrate their advantages by asymptotic theory and by means of a simulation study.
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Keywords
adaptive Lasso, asymptotic normality, bridge estimators, conservative model selection, heteroscedasticity, Lasso, oracle property