On the degrees of freedom of the lasso

• 成果类型: Article
• 署名作者: Zou, Hui; Hastie, Trevor; Tibshirani, Robert
• 署名单位: University of Minnesota System; University of Minnesota Twin Cities; Stanford University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/009053607000000127
• 发表日期: 2007
• 页码: 2173-2192
• 关键词: nonconcave penalized likelihood; adaptive model selection; variable selection; regression; shrinkage

摘要

We study the effective degrees of freedom of the lasso in the framework of Stein's unbiased risk estimation (SURE). We show that the number of nonzero coefficients is an unbiased estimate for the degrees of freedom of the lasso-a conclusion that requires no special assumption on the predictors. In addition, the unbiased estimator is shown to be asymptotically consistent. With these results on hand, various model selection criteria-C-p, AIC and BIC-are available, which, along with the LARS algorithm, provide a principled and efficient approach to obtaining the optimal lasso fit with the computational effort of a single ordinary least-squares fit.