vector, we sharpen and unify existing oracle inequalities for the Lasso and Dantzig selector. We derive oracle inequalities for target coefficient vectors with many small elements and smaller threshold levels than the universal threshold. These oracle inequalities provide sufficient conditions

Yi = g(Zi) + Wi, i = 1,..., n, where we wish to estimate the function g given the data under the assumption that the Wi are independent indentically distributed Gaussian error terms and g lies inside of some function space

The Dantzig selector performs variable selection and model fitting in linear regression. It uses an L1 penalty to shrink the regression coefficients towards zero, in a similar fashion to the Lasso. While both the Lasso and Dantzig selector potentially do a good job of selecting the correct

The Dantzig Selector is a recent approach to estimation in high-dimensional linear regression models with a large number of explanatory variables and a relatively small number of observations. As in the least absolute shrinkage and selection operator (LASSO), this approach sets certain regression

the Dantzig selector, proposed by Candes and Tao (2007), to screen important effects. A graphical procedure and an automated procedure are suggested to accompany with the method. Simulation shows that this method performs well compared to existing methods in the literature and is more efficient at estimating

We propose a Generalized Dantzig Selector (GDS) for linear models, in which any norm encoding the parameter structure can be leveraged for estimation. We investigate both computational and statistical aspects of the GDS. Based on conjugate proximal operator, a flexible inexact ADMM framework

Professors Candès and Tao are to be congratulated for their innovative and valuable contribution to high-dimensional sparse recovery and model selection. The analysis of vast data sets now commonly arising in scientific investigations poses many statistical challenges not present in smaller scale

ABSTRACT. We investigate the high-dimensional regression problem using adjacency matrices of unbalanced expander graphs. In this frame, we prove that the `2-prediction error and the `1-risk of the lasso and the Dantzig selector are optimal up to an explicit multiplicative constant. Thus we can

We develop a group of algorithms for variable selection using the accelerated failure time (AFT) models that are based on the synthesis of the Buckley–James estimating method and the Dantzig selector. In particular, first two algorithms are based on two modified Buckley–James estimating methods

The Dantzig selector performs variable selection and model fitting in linear regression. It uses an L1 penalty to shrink the regression coefficients towards zero, in a similar fashion to the lasso. While both the lasso and Dantzig selector potentially do a good job of selecting the correct