论文信息 - Discussion: The Dantzig selector: Statistical estimation when p is much larger than n

Discussion: The Dantzig selector: Statistical estimation when p is much larger than n

1. Introduction. This is a fascinating paper on an important topic: the choice of predictor variables in large-scale linear models. A previous paper in these pages attacked the same problem using the “LARS” algorithm (Efron, Hastie, Johnstone and Tibshirani [3]); actually three algorithms including the Lasso as middle case. There are tantalizing similarities between the Dantzig Selector (DS) and the LARS methods, but they are not the same and produce somewhat different models. We explore this relationship with the Lasso and LARS here. 2. Dantzig selector and the Lasso. The definition of the Dantzig selector (DS) in (1.7) can be re-expressed as

R. Tibshirani | T. Hastie | B. Efron

[1] R. Tibshirani. Regression Shrinkage and Selection via the Lasso , 1996 .

[2] Michael A. Saunders,et al. Atomic Decomposition by Basis Pursuit , 1998, SIAM J. Sci. Comput..

[3] M. R. Osborne,et al. A new approach to variable selection in least squares problems , 2000 .

[4] D. Madigan,et al. [Least Angle Regression]: Discussion , 2004 .

[5] S. Rosset,et al. Piecewise linear regularized solution paths , 2007, 0708.2197.

[6] Yaakov Tsaig,et al. Fast Solution of $\ell _{1}$ -Norm Minimization Problems When the Solution May Be Sparse , 2008, IEEE Transactions on Information Theory.