Sup-norm convergence rate and sign concentration property of Lasso and Dantzig estimators
Sup-norm convergence rate and sign concentration property of Lasso and Dantzig estimators
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DOI：
10.1214/08-ejs177
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发表时间：
2008-01-01
影响因子：
1.1
通讯作者：
Lounici, Karim
中科院分区：
文献类型：
--
作者：
Lounici, Karim
在高维线性回归模型的Gram矩阵上的相干性假设和两种不同的噪声假设下，得到了高维线性回归模型中Lasso估计和Dantzig估计的L(无穷)收敛速度。然后，我们证明了当目标向量的非零分量不太小时，适当选择阈值的Lasso和Dantzig门限估计同时具有符号集中性质。
We derive the l(infinity) convergence rate simultaneously for Lasso and Dantzig estimators in a high-dimensional linear regression model under a mutual coherence assumption on the Gram matrix of the design and two different assumptions on the noise: Gaussian noise and general noise with finite variance. Then we prove that simultaneously the thresholded Lasso and Dantzig estimators with a proper choice of the threshold enjoy a sign concentration property provided that the non-zero components of the target vector are not too small.