The Nonparanormal SKEPTIC
Han Liu (Johns Hopkins University), Fang Han (Johns Hopkins, University), Ming Yuan (Georgia Institute of Technology), John Lafferty, (University of Chicago), Larry Wasserman (Carnegie Mellon University)

TL;DR
This paper introduces a semiparametric method called nonparanormal skeptic for estimating high-dimensional graphical models, leveraging rank-based correlations to achieve optimal convergence rates, thus providing a robust alternative to Gaussian models.
Contribution
The paper develops a novel semiparametric estimation technique using rank-based correlations for high-dimensional graphical models, demonstrating optimal convergence rates.
Findings
Achieves optimal parametric convergence rates in high dimensions
Validates nonparanormal models as a safe alternative to Gaussian models
Uses Spearman's rho and Kendall's tau for estimation
Abstract
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.
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Taxonomy
TopicsStatistical Methods and Inference · Bayesian Modeling and Causal Inference · Advanced Statistical Methods and Models
