This article reviews the literature on sparse high-dimensional models and discusses some
applications in economics and finance. Recent developments in theory, methods, and …

This paper considers regularizing a covariance matrix of p variables estimated from n
observations, by hard thresholding. We show that the thresholded estimate is consistent in …

The paper proposes a method for constructing a sparse estimator for the inverse covariance
(concentration) matrix in high-dimensional settings. The estimator uses a penalized normal …

This article features online supplementary material. In this article, we propose a
computationally efficient approach—space (Sparse PArtial Correlation Estimation)—for …

This paper studies the sparsistency and rates of convergence for estimating sparse
covariance and precision matrices based on penalized likelihood with nonconvex penalty …

Statistical Foundations of Data Science gives a thorough introduction to commonly used
statistical models, contemporary statistical machine learning techniques and algorithms …

We consider the empirical risk minimization problem for linear supervised learning, with
regularization by structured sparsity-inducing norms. These are defined as sums of …

This paper considers the problem of estimating a high dimensional inverse covariance
matrix that can be well approximated by “sparse” matrices. Taking advantage of the …

We propose a new class of generalized thresholding operators that combine thresholding
with shrinkage, and study generalized thresholding of the sample covariance matrix in high …

Penalized likelihood methods are fundamental to ultrahigh dimensional variable selection.
How high dimensionality such methods can handle remains largely unknown. In this paper …