Sparsity-constrained Gaussian copula graphical models

{Monte Carlo simulations and real-data financial network applications demonstrate improved graph recovery and estimation under Gaussian copula graphical models.} Gaussian graphical models learn conditional dependencies through a sparse precision matrix, but the normality assumption is frequently unjustified in practice. Under the nonparanormal model, SKEPTIC [Liu H, Han F, Yuan M, et al. High-dimensional semiparametric gaussian copula graphical models. Ann Stat. 2012;40(4):2293–2326. doi: 10.1214/12-AOS1037] uses rank-based statistics to estimate the latent correlation, but the resulting matrix may be indefinite, destabilizing estimation and prompting additional stabilization steps. We propose a two-stage SKEPTIC–SCGlasso procedure that combines Kendall's τ correlation estimator with SCGlasso [Fulci A, Paterlini S, Taufer E. An ℓ0-constrained and ℓ1-regularized estimator for graphical models. Stat Comput. 2026;36:60. doi: 10.1007/s11222-025-10817-1], an ℓ0-constrained and ℓ1-regularized estimator of sparse precision matrices. SCGlasso controls sparsity through an explicit edge budget and uses an ℓ1-penalty for numerical stability. In Monte Carlo experiments across several topologies and sample sizes, the proposed pipeline improves Frobenius error and graph recovery relative to Glasso, SCAD, and MCP, with particularly robust performance when the sample size is small relative to, or comparable with, the dimension, the regime in which the plug-in correlation estimate is most frequently indefinite. Applications to the French 49 industry portfolios and to the constituents of the Nikkei 225 index yield interpretable networks with sectoral structure.