A constraint-based algorithm for nonparanormal data

The PC algorithm is the most known constraint-based algorithm for selecting a directed acyclic graph. For Gaussian distributions, it infers the structure using conditional independence tests based on Pearson correlation coefficients. The Rank PC algorithm, based on Spearman correlation, has been recently proposed when data are drawn from a Gaussian Copula model. We propose a modified version of the Grow-Shrink algorithm, based on the recovery of the Markov blanket of the nodes and on the Spearman correlation. In simulations, our Copula Grow-Shrink algorithm performs better than PC and Rank PC ones, according to structural Hamming distance.