Open Access
October 2007 On the “degrees of freedom” of the lasso
Hui Zou, Trevor Hastie, Robert Tibshirani
Ann. Statist. 35(5): 2173-2192 (October 2007). DOI: 10.1214/009053607000000127


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—Cp, 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.


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Hui Zou. Trevor Hastie. Robert Tibshirani. "On the “degrees of freedom” of the lasso." Ann. Statist. 35 (5) 2173 - 2192, October 2007.


Published: October 2007
First available in Project Euclid: 7 November 2007

zbMATH: 1126.62061
MathSciNet: MR2363967
Digital Object Identifier: 10.1214/009053607000000127

Primary: 62J05 , 62J07 , 90C46

Keywords: Degrees of freedom , LARS algorithm , Lasso , Model selection , SURE , unbiased estimate

Rights: Copyright © 2007 Institute of Mathematical Statistics

Vol.35 • No. 5 • October 2007
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