2019/04/09 by Yuehan Yang, Yang, Yuehan, Siwei Xia +3
Decision Sciences · Mathematics · #Advanced Statistical Methods and Models #FOS: Computer and information sciences #Methodology (stat.ME) #Multi-Criteria Decision Making #Statistical Methods and Inference
paper · pdf · doi:10.48550/arxiv.1904.04664
openalex publication_date 2019/04/09 · openalex created_date 2019/04/25 · openalex updated_date 2026/07/28
This paper considers a high-dimensional linear regression problem where there are complex correlation structures among predictors. We propose a graph-constrained regularization procedure, named Sparse Laplacian Shrinkage with the Graphical Lasso Estimator (SLS-GLE). The procedure uses the estimated precision matrix to describe the specific information on the conditional dependence pattern among predictors, and encourages both sparsity on the regression model and the graphical model. We introduce the Laplacian quadratic penalty adopting the graph information, and give detailed discussions on the advantages of using the precision matrix to construct the Laplacian matrix. Theoretical properties and numerical comparisons are presented to show that the proposed method improves both model interpretability and accuracy of estimation. We also apply this method to a financial problem and prove that the proposed procedure is successful in assets selection.