The Nonparanormal SKEPTIC
This provides a robust method for statistical modeling in high-dimensional data analysis, offering a safe alternative to Gaussian graphical models even under Gaussian assumptions, though it is incremental as it builds on existing nonparanormal frameworks.
The paper tackles the problem of estimating high-dimensional undirected graphical models by proposing a semiparametric approach called the nonparanormal skeptic, which uses nonparametric rank-based correlation estimators and achieves optimal parametric convergence rates in graph and parameter estimation.
We propose a semiparametric approach, named nonparanormal skeptic, for estimating high dimensional undirected graphical models. In terms of modeling, we consider the nonparanormal family proposed by Liu et al (2009). In terms of estimation, we exploit nonparametric rank-based correlation coefficient estimators including the Spearman's rho and Kendall's tau. In high dimensional settings, we prove that the nonparanormal skeptic achieves the optimal parametric rate of convergence in both graph and parameter estimation. This result suggests that the nonparanormal graphical models are a safe replacement of the Gaussian graphical models, even when the data are Gaussian.