Related papers: Assumptionless consistency of the Lasso

High-dimensional linear regression is a fundamental tool in modern statistics, particularly when the number of predictors exceeds the sample size. The classical Lasso, which relies on the squared loss, performs well under Gaussian noise…

Sparse linear regression is a central problem in high-dimensional statistics. We study the correlated random design setting, where the covariates are drawn from a multivariate Gaussian $N(0,\Sigma)$, and we seek an estimator with small…

In high-dimensional statistics, the Lasso is a cornerstone method for simultaneous variable selection and parameter estimation. However, its reliance on the squared loss function renders it highly sensitive to outliers and heavy-tailed…

Sparsity promoting norms are frequently used in high dimensional regression. A limitation of such Lasso-type estimators is that the optimal regularization parameter depends on the unknown noise level. Estimators such as the concomitant…

In this paper, we propose a triple (or double-debiased) Lasso estimator for inference on a low-dimensional parameter in high-dimensional linear regression models. The estimator is based on a moment function that satisfies not only first-…

Traditionally regression analysis answers questions about the relationships among variables based on the assumption that the observation values of variables are precise numbers. It has long been dominated by least squares techniques, mostly…

Detecting changepoints in a one-dimensional signal is a classical yet fundamental problem. The fused lasso provides an elegant convex formulation that produces a stepwise estimate of the mean, but quantifying the uncertainty of the detected…

We study high-dimensional regression with missing entries in the covariates. A common strategy in practice is to \emph{impute} the missing entries with an appropriate substitute and then implement a standard statistical procedure acting as…

Large-scale empirical data, the sample size and the dimension are high, often exhibit various characteristics. For example, the noise term follows unknown distributions or the model is very sparse that the number of critical variables is…

Recent studies in the literature have paid much attention to the sparsity in linear classification tasks. One motivation of imposing sparsity assumption on the linear discriminant direction is to rule out the noninformative features, making…

Classically, statistical datasets have a larger number of data points than features ($n > p$). The standard model of classical statistics caters for the case where data points are considered conditionally independent given the parameters.…

We introduce c-lasso, a Python package that enables sparse and robust linear regression and classification with linear equality constraints. The underlying statistical forward model is assumed to be of the following form: \[ y = X \beta +…

This paper examines LASSO, a widely-used $L_{1}$-penalized regression method, in high dimensional linear predictive regressions, particularly when the number of potential predictors exceeds the sample size and numerous unit root regressors…

For statistical inference on regression models with a diverging number of covariates, the existing literature typically makes sparsity assumptions on the inverse of the Fisher information matrix. Such assumptions, however, are often…

We derive new theoretical results on the properties of the adaptive least absolute shrinkage and selection operator (adaptive lasso) for time series regression models. In particular, we investigate the question of how to conduct finite…

We propose a minimum distance estimation method for robust regression in sparse high-dimensional settings. The traditional likelihood-based estimators lack resilience against outliers, a critical issue when dealing with high-dimensional…

The lasso procedure is ubiquitous in the statistical and signal processing literature, and as such, is the target of substantial theoretical and applied research. While much of this research focuses on the desirable properties that lasso…

Nonlinear regression analysis is a popular and important tool for scientists and engineers. In this article, we introduce theories and methods of nonlinear regression and its statistical inferences using the frequentist and Bayesian…

Explanatory variables in a predictive regression typically exhibit low signal strength and various degrees of persistence. Variable selection in such a context is of great importance. In this paper, we explore the pitfalls and possibilities…

This note develops an analysis of the Lasso \( \hat b\) in linear models without any sparsity or L1 assumption on the true regression vector, in the proportional regime where dimension \( p \) and sample \( n \) are of the same order. Under…