2007/12/06 by Hui Zou, Trevor Hastie, Robert Tibshirani · 1 citation
Mathematics · #math.ST #stat.TH #msc:62J05 #msc:62J07 #msc:90C46
paper · pdf · doi:10.1214/009053607000000127
published as Annals of Statistics 2007, Vol. 35, No. 5, 2173-2192 · Published in at http://dx.doi.org/10.1214/009053607000000127 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)
arxiv created 2007/12/06 · arxiv updated 2009/12/01
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.