Asymptotic properties for combined L1 and concave regularization

• 成果类型: Article
• 署名作者: Fan, Yingying; Lv, Jinchi
• 署名单位: University of Southern California
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/ast047
• 发表日期: 2014
• 页码: 5770
• 关键词: nonconcave penalized likelihood; variable selection; Lasso

摘要

Two important goals of high-dimensional modelling are prediction and variable selection. In this article, we consider regularization with combined L-1 and concave penalties, and study the sampling properties of the global optimum of the suggested method in ultrahigh-dimensional settings. The L-1 penalty provides the minimum regularization needed for removing noise variables in order to achieve oracle prediction risk, while a concave penalty imposes additional regularization to control model sparsity. In the linear model setting, we prove that the global optimum of our method enjoys the same oracle inequalities as the lasso estimator and admits an explicit bound on the false sign rate, which can be asymptotically vanishing. Moreover, we establish oracle risk inequalities for the method and the sampling properties of computable solutions. Numerical studies suggest that our method yields more stable estimates than using a concave penalty alone.