Abstract
In this paper, we consider the adaptive group Lasso in high-dimensional linear regression. Some extensions have been done with other fitting procedures, such as adaptive Lasso, nonconcave penalized likelihood and adaptive elastic-net. Under appropriate conditions, we establish the consistency and asymptotic normality, which means that the adaptive group Lasso shares the oracle property in high-dimensional linear regression when the number of group variables diverges with the sample size.
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