A flexible shrinkage operator for fussy grouped variable selection

UNCG Author/Contributor (non-UNCG co-authors, if there are any, appear on document)
Xiaoli Gao, Associate Professor (Creator)
The University of North Carolina at Greensboro (UNCG )
Web Site: http://library.uncg.edu/

Abstract: Existing grouped variable selection methods rely heavily on prior group information, thus they may not be reliable if an incorrect group assignment is used. In this paper, we propose a family of shrinkage variable selection operators by controlling the k-th largest norm (KAN). The proposed KAN method exhibits some flexible group-wise variable selection naturally even though no correct prior group information is available. We also construct a group KAN shrinkage operator using a composite of KAN constraints. Neither ignoring nor relying completely on prior group information, the group KAN method has the flexibility of controlling within group strength and therefore can reduce the effect caused by incorrect group information. Finally, we investigate an unbiased estimator of the degrees of freedom for (group) KAN estimates in the framework of Stein’s unbiased risk estimation. Extensive simulation studies and real data analysis are performed to demonstrate the advantage of KAN and group KAN over the LASSO and group LASSO, respectively.

Additional Information

Statistical Papers
Language: English
Date: 2016
Degrees of freedom, Group shrinkage, k-th largest norm, Shrinkage estimator, Variable selection

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