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.

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关于源为无穷惩罚导数的凹罚估计的强预言性质

我们针对一类在原点具有无限导数的凹惩罚在高维线性回归模型中研究凹惩罚估计的强大预言性。该类包括桥接和对数惩罚作为典型示例。众所周知，惩罚的无限导数对于弱的先兆属性不是问题，但会阻止强的先兆属性。我们证明了原点附近的平滑线性化足以满足该类的强预言性质。