Enmsp: an elastic-net multi-step screening procedure for high-dimensional regression

To improve the estimation efficiency of high-dimensional regression problems, penalized regularization is routinely used. However, accurately estimating the model remains challenging, particularly in the presence of correlated effects, wherein irrelevant covariates exhibit strong correlation with relevant ones. This situation, referred to as correlated data, poses additional complexities for model estimation. In this paper, we propose the elastic-net multi-step screening procedure (EnMSP), an iterative algorithm designed to recover sparse linear models in the context of correlated data. EnMSP uses a small repeated penalty strategy to identify truly relevant covariates in a few iterations. Specifically, in each iteration, EnMSP enhances the adaptive lasso method by adding a weighted l2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$l_2$$\end{document} penalty, which improves the selection of relevant covariates. The method is shown to select the true model and achieve the l2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$l_2$$\end{document}-norm error bound under certain conditions. The effectiveness of EnMSP is demonstrated through numerical comparisons and applications in financial data.