Sup-norm convergence rate and sign concentration property of Lasso and Dantzig estimators

Details 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

2008-01-30

arxiv.org/abs/0801.4610v2

Electronic Journal of Statistics 2008, Vol. 2, 90-102

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.1214/08-EJS177 the Electronic Journal of Statistics (http://www.i-journals.org/ejs/) by t

Scientific paper

10.1214/08-EJS177

We derive the $l_{\infty}$ 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.

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