Discussion: A tale of three cousins: Lasso, L2Boosting and Dantzig

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Discussion of ``The Dantzig selector: Statistical estimation when $p$ is much larger than $n$'' by Emmanuel Candes and Terence Tao [math/0506081]

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Estimation Stability With Cross-Validation (ESCV) (2013, background): “Despite the diﬀerence in nature, numerous works have shown these regularization methods, at least in the context of the linear model, are intrinsically related (Efron et al. 2004; Zhao and Yu 2007; Meinshausen et al. 2007).”
Least angle and ℓ1 penalized regression: A review (2008, background): “However, Efron et al. (2007) and Meinshausen et al. (2007) argue that LASSO is preferable to the Danzig selector for two reasons: implementation and performance.”
A Selective Overview of Variable Selection in High Dimensional Feature Space (2009, background): “For example, Meinshausen, Rocha and Yu (2007) give a diagonal dominance condition of the p × p matrix ( X T X ) − 1 that ensures their equivalence.”
DASSO: connections between the Dantzig selector and lasso (2009, methodology): “We would like to point out that, after the paper was submitted, two recent references, Bickel et al. (2008) and Meinshausen et al. (2007), came to our attention.”
LASSO-TYPE RECOVERY OF SPARSE REPRESENTATIONS FOR HIGH-DIMENSIONAL DATA (2008, result): “This comes maybe as no surprise since the formulation of the “Dantzig selector” is quite similar to the Lasso [24].”