Discussion: The Dantzig selector: Statistical estimation when p is much larger than n
By Bradley Efron, Trevor J. Hastie, Robert Tibshirani. 2007
92 citations recorded by the source corpus.
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
Subfields: Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/b84b8bd8daeaa786f1f5e2bb0b06313568198b34
How researchers see this paper
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In Statistics and Probability
- Cun-Hui Zhang
- Jinchi Lv
- Jianqing Fan
- Peter Radchenko
- Peter Buhlmann
- Hui Zou
- Gareth M. James
- Yingying Fan
Citations in the corpus
- A generalized Dantzig selector with shrinkage tuning (2009, result): “This similarity is consistent with the theory and empirical results in Efron et al. (2007), Meinshausen et al. (2008), James et al. (2008a) and others, which show strong connections between the Lasso and Dantzig selector.”
- Rate Minimaxity of the Lasso and Dantzig Selector for the lq Loss in lr Balls (2010, background): “Efron, Hastie, and Tibshirani (2007) questioned whether a similar performance bound holds for the Lasso estimator as well.”
- A Selective Overview of Variable Selection in High Dimensional Feature Space (2009, background): “See Fan and Lv (2008) and Cai and Lv (2007) for more discussions.”
- Sure independence screening for ultrahigh dimensional feature space (2006, background): “It follows from (47) and (48) and the choice of c̃1 and c̃2 above that P (A) ≤ 2e−Cn and P (B) ≤ 2e−Cp.”
- DASSO: connections between the Dantzig selector and lasso (2009, unknown): “Other researchers have noted similar relationships (Efron et al., 2007).”