Simultaneous analysis of Lasso and Dantzig selector
Bickel, Peter J. ; Ritov, Ya’acov ; Tsybakov, Alexandre B.
Ann. Statist., Tome 37 (2009) no. 1, p. 1705-1732 / Harvested from Project Euclid
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We show that, under a sparsity scenario, the Lasso estimator and the Dantzig selector exhibit similar behavior. For both methods, we derive, in parallel, oracle inequalities for the prediction risk in the general nonparametric regression model, as well as bounds on the ℓp estimation loss for 1≤p≤2 in the linear model when the number of variables can be much larger than the sample size.
Publié le : 2009-08-15
Classification:  Linear models,  model selection,  nonparametric statistics,  60K35,  62G08,  62C20,  62G05,  62G20 
@article{1245332830,
     author = {Bickel, Peter J. and Ritov, Ya'acov and Tsybakov, Alexandre B.},
     title = {Simultaneous analysis of Lasso and Dantzig selector},
     journal = {Ann. Statist.},
     volume = {37},
     number = {1},
     year = {2009},
     pages = { 1705-1732},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1245332830}
}

Bickel, Peter J.; Ritov, Ya’acov; Tsybakov, Alexandre B. Simultaneous analysis of Lasso and Dantzig selector. Ann. Statist., Tome 37 (2009) no. 1, pp.  1705-1732. http://gdmltest.u-ga.fr/item/1245332830/