B0292
Title: A novel approach of high dimensional linear hypothesis testing problem
Authors: Zhe Zhang - The University of North Carolina at Chapel Hill (United States) [presenting]
Runze Li - The Pennsylvania State University (United States)
Xiufan Yu - University of Notre Dame (United States)
Abstract: An innovative double power-enhanced testing procedure is proposed for inference on high-dimensional linear hypotheses in high-dimensional regression models. Through a projection approach that aims to separate useful inferential information from the nuisance one, the proposed test accurately accounts for the impact of high-dimensional nuisance parameters. This projection procedure enables transforming the problem of interest into a test on moment conditions, from which a U-statistic-based test is constructed that is applicable in simultaneous inference on multiple or a diverging number of linear hypotheses. The theoretical studies prove that under some regularity conditions, the plug-in test statistic converges to its oracle counterpart, acting as well as if the nuisance parameters were known in advance. Asymptotic null normality is established to provide convenient tools for statistical inference, accompanied by rigorous power analysis. To further strengthen the testing power, two power enhancement techniques are developed to boost the power from two distinct aspects respectively, and integrate them into one powerful testing procedure to achieve double power enhancement. The power enhancement properties are validated at every step of the power enhancement procedure. The finite-sample performance is demonstrated using simulation studies, and an application to identifying associations between gene sets and a cancer-related gene expression.
