On the strong oracle property of concave penalized estimators with infinite penalty derivative at the origin

Abstract

We study the strong oracle property of concave penalized estimators in the high-dimensional linear regression model for a class of concave penalties that have infinite derivative at the origin. The class includes the bridge and log penalties as typical examples. It is known that infinite derivative of the penalty is not a problem for the weak oracle property but prevents the strong oracle property. We prove that a smooth linearization near the origin is sufficient for the strong oracle property for the class.