  Knockoffs is a new framework for controlling the false discovery rate (FDR)
in multiple hypothesis testing problems involving complex statistical models.
While there has been great emphasis on Type-I error control, Type-II errors
have been far less studied. In this paper we analyze the false negative rate
or, equivalently, the power of a knockoff procedure associated with the Lasso
solution path under an i.i.d. Gaussian design, and find that knockoffs
asymptotically achieve close to optimal power with respect to an omniscient
oracle. Furthermore, we demonstrate that for sparse signals, performing model
selection via knockoff filtering achieves nearly ideal prediction errors as
compared to a Lasso oracle equipped with full knowledge of the distribution of
the unknown regression coefficients. The i.i.d. Gaussian design is adopted to
leverage results concerning the empirical distribution of the Lasso estimates,
which makes power calculation possible for both knockoff and oracle procedures.
