Estimation of a sparse group of sparse vectors

• 成果类型: Article
• 署名作者: Abramovich, Felix; Grinshtein, Vadim
• 署名单位: Tel Aviv University; Open University Israel
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/ass082
• 发表日期: 2013
• 页码: 355370
• 关键词: bayesian testimation; Optimal Rates; selection; regularization; regression

摘要

We consider estimating a sparse group of sparse normal mean vectors, based on penalized likelihood estimation with complexity penalties on the number of nonzero mean vectors and the numbers of their significant components, which can be performed by a fast algorithm. The resulting estimators are developed within a Bayesian framework and can be viewed as maximum a posteriori estimators. We establish their adaptive minimaxity over a wide range of sparse and dense settings. A simulation study demonstrates the efficiency of the proposed approach, which successfully competes with the sparse group lasso estimator.