The Nonparanormal SKEPTIC

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.