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A flexible shrinkage operator for fussy grouped variable selection

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  • Xiaoli Gao

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.

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  • Xiaoli Gao, 2018. "A flexible shrinkage operator for fussy grouped variable selection," Statistical Papers, Springer, vol. 59(3), pages 985-1008, September.
    • Handle: RePEc:spr:stpapr:v:59:y:2018:i:3:d:10.1007_s00362-016-0799-y
    DOI: 10.1007/s00362-016-0799-y
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    References listed on IDEAS

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    4. Kato, Kengo, 2009. "On the degrees of freedom in shrinkage estimation," Journal of Multivariate Analysis, Elsevier, vol. 100(7), pages 1338-1352, August.
    5. Ming Yuan & Yi Lin, 2006. "Model selection and estimation in regression with grouped variables," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(1), pages 49-67, February.
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