High dimensional statistical problems arise from diverse fields of scientific research and
technological development. Variable selection plays a pivotal role in contemporary statistical …

The limitations of the well‐known LASSO regression as a variable selector are tested when
there exists dependence structures among covariates. We analyse both the classic situation …

We develop results for the use of Lasso and post‐Lasso methods to form first‐stage
predictions and estimate optimal instruments in linear instrumental variables (IV) models …

We study full Bayesian procedures for high-dimensional linear regression under sparsity
constraints. The prior is a mixture of point masses at zero and continuous distributions …

The idea for this book came from the time the authors spent at the Statistics and Applied
Mathematical Sciences Institute (SAMSI) in Research Triangle Park in North Carolina …

We consider the orthogonal matching pursuit (OMP) algorithm for the recovery of a high-
dimensional sparse signal based on a small number of noisy linear measurements. OMP is …

Supplementary material for Least squares after model selection in high-dimensional sparse
models. The online supplemental article 2 contains a finite sample results for the estimation …

Oracle inequalities and variable selection properties for the Lasso in linear models have
been established under a variety of different assumptions on the design matrix. We show in …

Supplementary material to “Estimation bounds and sharp oracle inequalities of regularized
procedures with Lipschitz loss functions”. Section 6 gives the proof of the main results …

Sparse estimation methods are aimed at using or obtaining parsimonious representations of
data or models. While naturally cast as a combinatorial optimization problem, variable or …