A dual-penalized approach to hypothesis testing in high-dimensional linear mediation models

The field of mediation analysis, specifically high-dimensional mediation analysis, has been arousing great interest due to its applications in genetics, economics and other areas. Mediation analysis aims to investigate how exposure variables influence outcome variable via mediators, and it is categorized into direct and indirect effects based on whether the influence is mediated. A novel hypothesis testing method, called the dual-penalized method, is proposed to test direct and indirect effects. This method offers mild conditions and sound theoretical properties. Additionally, the asymptotic distributions of the proposed estimators are established to perform hypothesis testing. Results from simulation studies demonstrate that the dual-penalized method is highly effective, especially in weak signal settings. Further more, the application of this method to the childhood trauma data set reveals a new mediator with a credible basis in biological processes.