Adjusting the Benjamini–Hochberg method for controlling the false discovery rate in knockoff-assisted variable selection

Summary

We consider the knockoff-based multiple testing set-up of Barber & Candès (2015). for variable selection in multiple regression. The method of Benjamini & Hochberg (1995) and an adaptive version of it are adjusted to this set-up, transforming them to valid |$p$|-value-based, false discovery rate-controlling methods that do not rely on specifying the correlation structure of the explanatory variables. Simulations and real data applications show that the proposed methods are powerful competitors of the false discovery rate-controlling method of Barber & Candès (2015).