SIMULTANEOUS ANALYSIS OF LASSO AND DANTZIG SELECTOR

• 成果类型: Article
• 署名作者: Bickel, Peter J.; Ritov, Ya'acov; Tsybakov, Alexandre B.
• 署名单位: University of California System; University of California Berkeley; Hebrew University of Jerusalem; Institut Polytechnique de Paris; ENSAE Paris; Sorbonne Universite; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS)
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/08-AOS620
• 发表日期: 2009
• 页码: 1705-1732
• 关键词: statistical estimation; variable selection; least-squares; regression; aggregation; sparsity; larger

摘要

We show that, under a sparsity scenario, the Lasso estimator and the Dantzig selector exhibit similar behavior. Forboth methods, wederive, inparallel, oracle inequalities for the prediction risk in the general nonparametric regression model, as well as bounds on the e(p) estimation loss for 1 <= p <= 2 in the linear model when the number of variables can be Much larger than the sample size.