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A Unified Framework for Pattern Recovery in Penalized and Thresholded Estimation and its Geometry
We consider the framework of penalized estimation where the penalty term is given by a real-valued polyhedral gauge, which encompasses methods such as LASSO (and many variants thereof such as the generalized LASSO), SLOPE, OSCAR, PACS and others.
Confidence Sets Based on Thresholding Estimators in High-Dimensional Gaussian Regression Models
Asymptotically, the intervals based on the thresholding estimators are larger even by an order of magnitude when the estimators are tuned to perform consistent variable selection.
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