STRONG ORACLE OPTIMALITY OF FOLDED CONCAVE PENALIZED ESTIMATION.

ABSTRACT: Folded concave penalization methods have been shown to enjoy the strong oracle property for high-dimensional sparse estimation. However, a folded concave penalization problem usually has multiple local solutions and the oracle property is established only for one of the unknown local solutions. A challenging fundamental issue still remains that it is not clear whether the local optimum computed by a given optimization algorithm possesses those nice theoretical properties. To close this important theoretical gap in over a decade, we provide a unified theory to show explicitly how to obtain the oracle solution via the local linear approximation algorithm. For a folded concave penalized estimation problem, we show that as long as the problem is localizable and the oracle estimator is well beh

SUBMITTER: Fan J 

PROVIDER: S-EPMC4295817 | biostudies-literature | 2014 Jun

REPOSITORIES: biostudies-literature