  In 2015, Barber and Candes introduced a new variable selection procedure
called the knockoff filter to control the false discovery rate (FDR) and prove
that this method achieves exact FDR control. Inspired by the work of Barber and
Candes (2015), we propose and analyze a pseudo-knockoff filter that inherits
some advantages of the original knockoff filter and has more flexibility in
constructing its knockoff matrix. Moreover, we perform a number of numerical
experiments that seem to suggest that the pseudo knockoff filter with the half
Lasso statistic has FDR control and offers more power than the original
knockoff filter with the Lasso Path or the half Lasso Statistic for the
numerical examples that we consider in this paper. Although we cannot establish
rigorous FDR control for the pseudo knockoff filter, we provide some partial
analysis of the pseudo knockoff filter with the half Lasso statistic and
establish a uniform FDP bound and an expectation inequality.
