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As the power of FDR control methods for high-dimensional variable selectionshas been mostly evaluated empirically, we focus here on theoretical poweranalyses of two recent such methods, the knockoff filter and the Gaussianmirror. We adopt the Rare/Weak signal model, popular in multiple testing andvariable selection literature, and characterize the rate of convergence of thenumber of false positives and the number of false negatives of FDR controlmethods for particular classes of designs.  Our analyses lead to several noteworthy discoveries. First, the choice of thesymmetric statistic in FDR control methods crucially affects the power. Second,with a proper symmetric statistic, the operation of adding "noise" to achieveFDR control yields almost no loss of power compared with its prototype, atleast for some special classes of designs. Third, the knockoff filter andGaussian mirror have comparable power for orthogonal designs, but they behavedifferently for non-orthogonal designs. We study the block-wise diagonaldesigns and show that the knockoff filter has a higher power when theregression coefficient vector is extremely sparse, and the Gaussian mirror hasa higher power when the coefficient vector is moderately sparse.

Power of FDR Control Methods: The Impact of Ranking Algorithm, Tampered Design, and Symmetric Statistic