Variable selection procedures from multiple testing

Variable selection has played an important role in statistical learning and scientific discoveries during the past ten years, and multiple testing is a fundamental problem in statistical inference and also has wide application in many scientific fields. Significant advances have been achieved in both areas. This study attempts to find a connection between adaptive LASSO (least absolute shrinkage and selection operator) and multiple testing procedures in linear regression models. We also propose procedures based on multiple testing methods to select variables and control the selection error rate, i.e., the false discovery rate. Simulation studies demonstrate that the proposed methods show good performance relative to controlling the selection error rate under a wide range of settings.