This paper introduces an estimator of the relative directed distance between
an estimated model and the true model, based on the Kulback-Leibler divergence
and is motivated by the generalized information criterion proposed by Konishi
and Kitagawa. This estimator can be used to select model in penalized Gaussian
copula graphical models. The use of this estimator is not feasible for
high-dimensional cases. However, we derive an efficient way to compute this
estimator which is feasible for the latter class of problems. Moreover, this
estimator is, generally, appropriate for several penalties such as lasso,
adaptive lasso and smoothly clipped absolute deviation penalty. Simulations
show that the method performs similarly to KL oracle estimator and it also
improves BIC performance in terms of support recovery of the graph.
Specifically, we compare our method with Akaike information criterion, Bayesian
information criterion and cross validation for band, sparse and dense network
structures