Related papers: Statistical inference for high dimensional regress…
The aim of this paper is to present a new estimation procedure that can be applied in many statistical frameworks including density and regression and which leads to both robust and optimal (or nearly optimal) estimators. In density…
The Bayesian Lasso is constructed in the linear regression framework and applies the Gibbs sampling to estimate the regression parameters. This paper develops a new sparse learning model, named the Bayesian Lasso Sparse (BLS) model, that…
This paper proposes a theory for $\ell_1$-norm penalized high-dimensional $M$-estimators, with nonconvex risk and unrestricted domain. Under high-level conditions, the estimators are shown to attain the rate of convergence…
Inverse probability weighted estimators are the oldest and potentially most commonly used class of procedures for the estimation of causal effects. By adjusting for selection biases via a weighting mechanism, these procedures estimate an…
We propose a self-tuning $\sqrt{\mathrm {Lasso}}$ method that simultaneously resolves three important practical problems in high-dimensional regression analysis, namely it handles the unknown scale, heteroscedasticity and (drastic)…
Given $n$ noisy samples with $p$ dimensions, where $n \ll p$, we show that the multi-step thresholding procedure based on the Lasso -- we call it the {\it Thresholded Lasso}, can accurately estimate a sparse vector $\beta \in \R^p$ in a…
Data subject to heavy-tailed errors are commonly encountered in various scientific fields, especially in the modern era with explosion of massive data. To address this problem, procedures based on quantile regression and Least Absolute…
Completely randomized experiment is the gold standard for causal inference. When the covariate information for each experimental candidate is available, one typical way is to include them in covariate adjustments for more accurate treatment…
The lasso has become an important practical tool for high dimensional regression as well as the object of intense theoretical investigation. But despite the availability of efficient algorithms, the lasso remains computationally demanding…
In this study, we investigate the bias and variance properties of the debiased Lasso in linear regression when the tuning parameter of the node-wise Lasso is selected to be smaller than in previous studies. We consider the case where the…
We consider the least-square linear regression problem with regularization by the l1-norm, a problem usually referred to as the Lasso. In this paper, we present a detailed asymptotic analysis of model consistency of the Lasso. For various…
The high-dimensional linear model $y = X \beta^0 + \epsilon$ is considered and the focus is put on the problem of recovering the support $S^0$ of the sparse vector $\beta^0.$ We introduce Lasso-Zero, a new $\ell_1$-based estimator whose…
We consider a linear regression problem in a high dimensional setting where the number of covariates $p$ can be much larger than the sample size $n$. In such a situation, one often assumes sparsity of the regression vector, \textit i.e.,…
We study random designs that minimize the asymptotic variance of a de-biased lasso estimator when a large pool of unlabeled data is available but measuring the corresponding responses is costly. The optimal sampling distribution arises as…
In this article we investigate consistency of selection in regression models via the popular Lasso method. Here we depart from the traditional linear regression assumption and consider approximations of the regression function $f$ with…
This paper investigates the two-step estimation of a high dimensional additive regression model, in which the number of nonparametric additive components is potentially larger than the sample size but the number of significant additive…
In this paper, we consider the Group Lasso estimator of the covariance matrix of a stochastic process corrupted by an additive noise. We propose to estimate the covariance matrix in a high-dimensional setting under the assumption that the…
This paper investigates the effect of the design matrix on the ability (or inability) to estimate a sparse parameter in linear regression. More specifically, we characterize the optimal rate of estimation when the smallest singular value of…
High-dimensional compositional data are frequently encountered in many fields of modern scientific research. In regression analysis of compositional data, the presence of covariate measurement errors poses grand challenges for existing…
In high-dimensional sparse regression, the \textsc{Lasso} estimator offers excellent theoretical guarantees but is well-known to produce biased estimates. To address this, \cite{Javanmard2014} introduced a method to ``debias" the…