  Sorted L-One Penalized Estimator (SLOPE) is a relatively new convex
optimization procedure for selecting predictors in large data bases. Contrary
to LASSO, SLOPE has been proved to be asymptotically minimax in the context of
sparse high-dimensional generalized linear models. Additionally, in case when
the design matrix is orthogonal, SLOPE with the sequence of tuning parameters
$\lambda^{BH}$, corresponding to the sequence of decaying thresholds for the
Benjamini-Hochberg multiple testing correction, provably controls False
Discovery Rate in the multiple regression model. In this article we provide new
asymptotic results on the properties of SLOPE when the elements of the design
matrix are iid random variables from the Gaussian distribution. Specifically,
we provide the conditions, under which the asymptotic FDR of SLOPE based on the
sequence $\lambda^{BH}$ converges to zero and the power converges to 1. We
illustrate our theoretical asymptotic results with extensive simulation study.
We also provide precise formulas describing FDR of SLOPE under different loss
functions, which sets the stage for future results on the model selection
properties of SLOPE and its extensions.
