SIMULTANEOUS ANALYSIS OF LASSO AND DANTZIG SELECTOR

被引：1398

作者：

Bickel, Peter J. ^{[1
]}

Ritov, Ya'acov ^{[2
]}

Tsybakov, Alexandre B. ^{[3
,4
]}

机构：

[1] Univ Calif Berkeley, Dept Stat, Berkeley, CA 94720 USA

[2] Hebrew Univ Jerusalem, Fac Social Sci, Dept Stat, IL-91904 Jerusalem, Israel

[3] CREST, Stat Lab, F-92240 Malakoff, France

[4] Univ Paris 06, CNRS, UMR 1599, LPMA, F-75252 Paris 05, France

来源：

ANNALS OF STATISTICS | 2009年 / 37卷 / 04期

关键词：

Linear models; model selection; nonparametric statistics; STATISTICAL ESTIMATION; VARIABLE SELECTION; LEAST-SQUARES; REGRESSION; AGGREGATION; SPARSITY; LARGER;

D O I：

10.1214/08-AOS620

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We show that, under a sparsity scenario, the Lasso estimator and the Dantzig selector exhibit similar behavior. Forboth methods, wederive, inparallel, oracle inequalities for the prediction risk in the general nonparametric regression model, as well as bounds on the e(p) estimation loss for 1 <= p <= 2 in the linear model when the number of variables can be Much larger than the sample size.

引用

页码：1705 / 1732

页数：28

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