Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1148720 | Journal of Statistical Planning and Inference | 2007 | 8 Pages |
Abstract
Efromovich-Pinsker and Stein blockwise-shrinkage estimates are traditionally studied via upper-bound oracle inequalities, which bound the estimate's risk from above by the oracle's risk plus a remainder term. These bounds allow one to establish sufficient conditions for attaining the oracle's risk. To explore necessary conditions, this article develops a lower-bound oracle inequality, which bounds the estimate's risk from below by the oracle's risk minus a remainder term. In particular, the lower bound implies that thresholds must vanish for attaining the oracle's risk.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Sam Efromovich,