Global optimality of nonconvex penalized estimators

• 成果类型: Article
• 署名作者: Kim, Yongdai; Kwon, Sunghoon
• 署名单位: Seoul National University (SNU); University of Minnesota System; University of Minnesota Twin Cities
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asr084
• 发表日期: 2012
• 页码: 315325
• 关键词: VARIABLE SELECTION; likelihood

摘要

Nonconvex penalties such as the smoothly clipped absolute deviation or minimax concave penalties have desirable properties such as the oracle property, even when the dimension of the predictive variables is large. However, checking whether a given local minimizer has such properties is not easy since there can be many local minimizers. In this paper, we give sufficient conditions under which a local minimizer is unique, and show that the oracle estimator becomes the unique local minimizer with probability tending to one.