HIGH-DIMENSIONAL VARIABLE SELECTION

• 成果类型: Article
• 署名作者: Wasserman, Larry; Roeder, Kathryn
• 署名单位: Carnegie Mellon University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/08-AOS646
• 发表日期: 2009
• 页码: 2178-2201
• 关键词: lasso; regression; approximation; Consistency

摘要

This paper explores the following question: what kind of statistical guarantees can be given when doing variable selection in high-dimensional models? In particular, we look at the error rates and power of some multi-stage regression methods. In the first stage we fit a set of candidate models. In the second stage we select one model by cross-validation. In the third stage we use hypothesis testing to eliminate some variables. We refer to the first two stages as screening and the last stage as cleaning. We consider three screening methods: the lasso, marginal regression, and forward stepwise regression. Our method gives consistent variable selection under certain conditions.