  We introduce Graphical TREX (GTREX), a novel method for graph estimation in
high-dimensional Gaussian graphical models. By conducting neighborhood
selection with TREX, GTREX avoids tuning parameters and is adaptive to the
graph topology. We compare GTREX with standard methods on a new simulation
set-up that is designed to assess accurately the strengths and shortcomings of
different methods. These simulations show that a neighborhood selection scheme
based on Lasso and an optimal (in practice unknown) tuning parameter
outperforms other standard methods over a large spectrum of scenarios.
Moreover, we show that GTREX can rival this scheme and, therefore, can provide
competitive graph estimation without the need for tuning parameter calibration.
