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

The knockoff-based multiple testing setup of Barber & Candes (2015) for variable selection in multiple regression where sample size is as large as the number of explanatory variables is considered. The method of Benjamini & Hochberg (1995) based on ordinary least squares estimates of the regression coefficients is adjusted to the setup, transforming it to a valid p-value based false discovery rate controlling method not relying on any specific correlation structure of the explanatory variables. Simulations and real data applications show that our proposed method that is agnostic to {\pi}0, the proportion of unimportant explanatory variables, and a data-adaptive version of it that uses an estimate of {\pi}0 are powerful competitors of the false discovery rate controlling method in Barber & Candes (2015).