A General Theory of Hypothesis Tests and Confidence Regions for Sparse High Dimensional Models

Understand

We consider the problem of uncertainty assessment for low dimensional components in high dimensional models.

• Specifically, we propose a decorrelated score function to handle the impact of high dimensional nuisance parameters.
• We consider both hypothesis tests and confidence regions for generic penalized M-estimators.
• Unlike most existing inferential methods which are tailored for individual models, our approach provides a general framework for high dimensional inference and is applicable to a wide range of applications.