the estimation error of the Lasso under two different sets of conditions on the covariates as well as the error terms … constants. These results are then used to show that the Lasso can be consistent in even very large models where the number of … regressors increases at an exponential rate in the sample size. Conditions under which the Lasso does not discard any relevant …

with Bayesian Markov Chain Monte Carlo. The resulting model is equivalent to the frequentist lasso procedure. A … covariates is provided by the approach. An implementation of the lasso procedure for binary quantile regression models is …

We propose the Bayesian adaptive Lasso (BaLasso) for variable selection and coefficient estimation in linear regression … hierarchical Bayesian interpretation of the Lasso. Our formulation also permits prediction using a model averaging strategy. We …

This paper establishes non-asymptotic oracle inequalities for the prediction error and estimation accuracy of the LASSO … in stationary vector autoregressive models. These inequalities are used to establish consistency of the LASSO even when … excluded. Next, non-asymptotic probabilities are given for the Adaptive LASSO to select the correct sign pattern (and hence the …

setting, several estimators such as the LASSO (Tibshirani, 1996) and the Dantzig Selector (Candes and Tao, 2007) are known to … satisfy interesting properties whenever the vector β∗ is sparse. Interestingly, both the LASSO and the Dantzig Selector can be … for the LASSO. For a well chosen s>0, this set is actually a confidence region for β∗. In this paper, we investigate the …