Simultaneous analysis of Lasso and Dantzig selector.
Peter Bickel, Yaac'ov Ritov and Alexandre Tsybakov
Annals of Statistics
We exhibit an approximate equivalence between the Lasso estimator
and Dantzig selector. For both methods we derive parallel oracle
inequalities for the prediction risk in the general nonparametric
regression model, as well as bounds on the $\ell_p$ estimation loss
for $1\le p\le 2$ in the linear model when the number of variables
can be much larger than the sample size.