  Recently, a special case of precision matrix estimation based on a
distributionally robust optimization (DRO) framework has been shown to be
equivalent to the graphical lasso. From this formulation, a method for choosing
the regularization term, i.e., for graphical model selection, was proposed. In
this work, we establish a theoretical connection between the confidence level
of graphical model selection via the DRO formulation and the asymptotic
family-wise error rate of estimating false edges. Simulation experiments and
real data analyses illustrate the utility of the asymptotic family-wise error
rate control behavior even in finite samples.
