Simultaneous analysis of Lasso and Dantzig selector

Details Simultaneous analysis of Lasso and Dantzig selector Simultaneous analysis of Lasso and Dantzig selector

2008-01-07

arxiv.org/abs/0801.1095v3

The Annals of Statistics 2009, Vol. 37, No. 4, 1705-1732

Mathematics

Statistics Theory

Noramlization factor corrected

Scientific paper

10.1214/08-AOS620

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.

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