Local and Global Inference for High Dimensional Nonparanormal Graphical Models

Abstract

This paper proposes a unified framework to quantify local and global inferential uncertainty for high dimensional nonparanormal graphical models. In particular, we consider the problems of testing the presence of a single edge and constructing a uniform confidence subgraph. Due to the presence of unknown marginal transformations, we propose a pseudo likelihood based inferential approach. In sharp contrast to the existing high dimensional score test method, our method is free of tuning parameters given an initial estimator, and extends the scope of the existing likelihood based inferential framework. Furthermore, we propose a U-statistic multiplier bootstrap method to construct the confidence subgraph. We show that the constructed subgraph is contained in the true graph with probability greater than a given nominal level. Compared with existing methods for constructing confidence subgraphs, our method does not rely on Gaussian or sub-Gaussian assumptions. The theoretical properties of the proposed inferential methods are verified by thorough numerical experiments and real data analysis.

58 pages, 4 figures, 2 tables

References in corpus (11)

• Asymptotic normality and optimalities in estimation of large Gaussian graphical models
• Regularized M-estimators with nonconvexity: Statistical and algorithmic theory for local optima
• Stability Approach to Regularization Selection (StARS) for High Dimensional Graphical Models
• Multiple Testing and Error Control in Gaussian Graphical Model Selection
• Model Selection Through Sparse Maximum Likelihood Estimation
• Sparse Matrix Inversion with Scaled Lasso
• Exact Post-Selection Inference for Sequential Regression Procedures
• High-dimensional Sparse Inverse Covariance Estimation using Greedy Methods
• A General Theory of Hypothesis Tests and Confidence Regions for Sparse High Dimensional Models
• Estimating Undirected Graphs Under Weak Assumptions
• High Dimensional Semiparametric Latent Graphical Model for Mixed Data

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