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

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  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.
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