A flexible shrinkage operator for fussy grouped variable selection
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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.
KeywordsDegrees of freedom Group shrinkage k-th largest norm Shrinkage estimator Variable selection
The author wants to thank Sijian Wang and Yuan Wu for their valuable comments and Jonathan Rowell for his professional proofreading. She also would like to thank the reviewers for their helpful and constructive comments for improvement of the manuscript. The author gratefully acknowledges Simons Foundation (#359337) and UNC Greensboro (New Faculty Grant) for their support in this Project.
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