Related papers: CoCoLasso for High-dimensional Error-in-variables …
Lasso is a celebrated method for variable selection in linear models, but it faces challenges when the variables are moderately or strongly correlated. This motivates alternative approaches such as using a non-convex penalty, adding a ridge…
In many problems involving generalized linear models, the covariates are subject to measurement error. When the number of covariates p exceeds the sample size n, regularized methods like the lasso or Dantzig selector are required. Several…
The covariance matrix plays a fundamental role in many modern exploratory and inferential statistical procedures, including dimensionality reduction, hypothesis testing, and regression. In low-dimensional regimes, where the number of…
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…
In this paper, we develop a novel high-dimensional coefficient estimation procedure based on high-frequency data. Unlike usual high-dimensional regression procedures such as LASSO, we additionally handle the heavy-tailedness of…
When we are interested in high-dimensional system and focus on classification performance, the $\ell_{1}$-penalized logistic regression is becoming important and popular. However, the Lasso estimates could be problematic when penalties of…
We propose a nonconvex estimator for joint multivariate regression and precision matrix estimation in the high dimensional regime, under sparsity constraints. A gradient descent algorithm with hard thresholding is developed to solve the…
Among the most popular variable selection procedures in high-dimensional regression, Lasso provides a solution path to rank the variables and determines a cut-off position on the path to select variables and estimate coefficients. In this…
Standard high-dimensional regression methods assume that the underlying coefficient vector is sparse. This might not be true in some cases, in particular in presence of hidden, confounding variables. Such hidden confounding can be…
In high-dimensional survival analysis, effective variable selection is crucial for both model interpretation and predictive performance. This paper investigates Cox regression with lasso and adaptive lasso penalties in genomic datasets…
The Lasso is one of the most important approaches for parameter estimation and variable selection in high dimensional linear regression. At the heart of its success is the attractive rate of convergence result even when $p$, the dimension…
Despite its prevalence in statistical datasets, heteroscedasticity (non-constant sample variances) has been largely ignored in the high-dimensional statistics literature. Recently, studies have shown that the Lasso can accommodate…
We consider high dimensional sparse regression, and develop strategies able to deal with arbitrary -- possibly, severe or coordinated -- errors in the covariance matrix $X$. These may come from corrupted data, persistent experimental…
In this paper, we propose a new method for estimation and constructing confidence intervals for low-dimensional components in a high-dimensional model. The proposed estimator, called Constrained Lasso (CLasso) estimator, is obtained by…
We propose Robust Lasso-Zero, an extension of the Lasso-Zero methodology, initially introduced for sparse linear models, to the sparse corruptions problem. We give theoretical guarantees on the sign recovery of the parameters for a slightly…
The lasso has been studied extensively as a tool for estimating the coefficient vector in the high-dimensional linear model; however, considerably less is known about estimating the error variance in this context. In this paper, we propose…
The Lasso is a prominent algorithm for variable selection. However, its instability in the presence of correlated variables in the high-dimensional setting is well-documented. Although previous research has attempted to address this issue…
Constrained least squares regression is an essential tool for high-dimensional data analysis. Given a partition $\mathcal{G}$ of input variables, this paper considers a particular class of nonconvex constraint functions that encourage the…
Post-Double-Lasso is becoming the most popular method for estimating linear regression models with many covariates when the purpose is to obtain an accurate estimate of a parameter of interest, such as an average treatment effect. However,…
The Lasso is a method for high-dimensional regression, which is now commonly used when the number of covariates $p$ is of the same order or larger than the number of observations $n$. Classical asymptotic normality theory does not apply to…