A Novel Approach of High Dimensional Linear Hypothesis Testing Problem

-statistic-based test that is applicable in simultaneous inference on a diverging number of linear hypotheses. We prove that under regularity conditions, the plug-in test statistic converges to its oracle counterpart, acting as well as if the nuisance parameters were known in advance. Moreover, we introduce an implementation-friendly version to tackle the computational challenge. Asymptotic null normality is established to provide convenient tools for statistical inference, accompanied by rigorous power analysis. To further strengthen the testing power, we develop two power enhancement techniques to boost the power from two distinct aspects respectively, and integrate them into one powerful testing procedure to achieve double power enhancement. The finite-sample performance is demonstrated using simulation studies, and an empirical analysis of a real data example.