Understand
This paper develops a framework for testing for associations in a possibly high-dimensional linear model where the number of features/variables may far exceed the number of observational units.
- In this framework, the observations are split into two groups, where the first group is used to screen for a set of potentially relevant variables, whereas the second is used for inference over this reduced set of variables; we also develop strategies for leveraging information from the first part of the data at the inference step for greater power.
- In our work, the inferential step is carried out by applying the recently introduced knockoff filter, which creates a knockoff copy-a fake variable serving as a control-for each screened variable.
- We prove that this procedure controls the directional false discovery rate (FDR) in the reduced model controlling for all screened variables; this says that our high-dimensional knockoff procedure 'discovers' important variables as well as the directions (signs) of their effects, in such a way that the expected proportion of wrongly chosen signs is below the user-specified level (thereby controlling a notion of Type S error averaged over the selected set).